From 1a0ba99f6bc0a6c08f78bc3e785b0704a81c28d1 Mon Sep 17 00:00:00 2001
From: Ian Jauslin <ian.jauslin@roma1.infn.it>
Date: Thu, 23 Jul 2015 14:55:49 +0000
Subject: Initial commit

---
 BBlog.sty                   |  38 +++++
 Gallavotti_Jauslin_2015.tex | 173 +++++++++++++++++++
 README                      |  49 ++++++
 bibliography.BBlog.tex      |  20 +++
 header.sty                  |  11 ++
 iansecs.sty                 | 402 ++++++++++++++++++++++++++++++++++++++++++++
 kiss.cls                    |  42 +++++
 toolbox.sty                 |  41 +++++
 8 files changed, 776 insertions(+)
 create mode 100644 BBlog.sty
 create mode 100644 Gallavotti_Jauslin_2015.tex
 create mode 100644 README
 create mode 100644 bibliography.BBlog.tex
 create mode 100644 header.sty
 create mode 100644 iansecs.sty
 create mode 100644 kiss.cls
 create mode 100644 toolbox.sty

diff --git a/BBlog.sty b/BBlog.sty
new file mode 100644
index 0000000..56f542b
--- /dev/null
+++ b/BBlog.sty
@@ -0,0 +1,38 @@
+%%
+%% BBlog bibliography related commands
+%%
+
+%% length used to display the bibliography
+\newlength{\rw}
+\setlength{\rw}{1.5cm}
+
+%% read header
+\IfFileExists{header.BBlog.tex}{\input{header.BBlog}}{}
+
+%% cite a reference
+\def\cite#1{%
+\ref{cite#1}%
+%% add entry to citelist after checking it has not already been added
+\ifcsname if#1cited\endcsname%
+\expandafter\if\csname if#1cited\endcsname%
+\else%
+\csname if#1citedtrue\endcsname%
+\immediate\write\@auxout{\noexpand\BBlogcite{#1}}%
+\fi%
+\else%
+\expandafter\newif\csname if#1cited\endcsname%
+\csname if#1citedtrue\endcsname%
+\immediate\write\@auxout{\noexpand\BBlogcite{#1}}%
+\fi%
+}
+%% an empty definition for the aux file
+\def\BBlogcite#1{}
+
+%% display the bibliography	
+\long\def\BBlography{
+  \newlength{\colw}
+  \setlength{\colw}{\textwidth}
+  \addtolength{\colw}{-\rw}
+  \IfFileExists{bibliography.BBlog.tex}{
+  \input{bibliography.BBlog}}{{\tt error: missing BBlog bibliography file}}
+}
diff --git a/Gallavotti_Jauslin_2015.tex b/Gallavotti_Jauslin_2015.tex
new file mode 100644
index 0000000..6c82ced
--- /dev/null
+++ b/Gallavotti_Jauslin_2015.tex
@@ -0,0 +1,173 @@
+\documentclass{kiss}
+% load packages
+\usepackage{header}
+% bibliography commands
+\usepackage{BBlog}
+% miscellaneous commands
+\usepackage{toolbox}
+% main style file
+\usepackage{iansecs}
+
+\begin{document}
+
+\bf\Large
+\hfil Kondo effect in the hierarchical $s-d$ model
+\normalsize
+\vskip20pt
+
+\hfil{Giovanni Gallavotti, Ian Jauslin}
+\vskip20pt
+\rm
+
+\hfil2015\par
+\hugeskip
+
+\leftskip20pt
+\rightskip20pt
+\small
+The $s-d$ model describes a chain of spin-1/2 electrons interacting magnetically with a two-level impurity. It was introduced to study the Kondo effect, in which the magnetic susceptibility of the impurity remains finite in the 0-temperature limit as long as the interaction of the impurity with the electrons is anti-ferromagnetic. A variant of this model was introduced by Andrei, which he proved was exactly solvable via Bethe Ansatz. A hierarchical version of Andrei's model was studied by Benfatto and the authors. In the present letter, that discussion is extended to a hierarchical version of the $s-d$ model.  The resulting analysis is very similar to the hierarchical Andrei model, though the result is slightly simpler.\par
+\leftskip0pt
+\rightskip0pt
+\normalsize
+
+\hugeskip
+
+\indent The $s-d$ model was introduced by Anderson [\cite{andSO}] and used by Kondo [\cite{konSF}] to study what would subsequently be called the {\it Kondo effect}. It describes a chain of electrons interacting with a fixed spin-1/2 magnetic impurity. One of the manifestations of the effect is that when the coupling is anti-ferrmoagnetic, the magnetic susceptibility of the impurity remains finite in the 0-temperature limit, whereas it diverges for ferromagnetic and for vanishing interactions.\par
+
+\indent A modified version of the $s-d$ model was introduced by Andrei [\cite{andEZ}], which was shown to be exactly solvable by Bethe Ansatz. In [\cite{bgjOFi}], a hierarchical version of Andrei's model was introduced and shown to exhibit a Kondo effect. In the present letter, we show how the argument can be adapted to the $s-d$ model.\par
+
+\indent We will show that in the hierarchical $s-d$ model, the computation of the susceptibility reduces to iterating an {\it explicit} map relating 6 {\it running coupling constants} (rccs), and that this map can be obtained by restricting the flow equation for the hierarchical Andrei model [\cite{bgjOFi}] to one of its invariant manifolds. The physics of both models are therefore very closely related, as had already been argued in [\cite{bgjOFi}]. This is particularly noteworthy since, at 0-field, the flow in the hierarchical Andrei model is relevant, whereas it is marginal in the hierarchical $s-d$ model, which shows that the relevant direction carries little to no physical significance.\par
+\bigskip
+
+\indent The $s-d$ model [\cite{konSF}] represents a chain of non-interacting spin-1/2 fermions, called {\it electrons}, which interact with an isolated spin-1/2 {\it impurity} located at site 0. The Hilbert space of the system is $\mathcal F_L\otimes\mathbb C^2$ in which $\mathcal F_L$ is the Fock space of a length-$L$ chain of spin-1/2 fermions (the electrons) and $\mathbb C^2$ is the state space for the two-level impurity. The Hamiltonian, in the presence of a magnetic field of amplitude $h$ in the direction $\bm\omega\equiv(\bm\omega_1,\bm\omega_2,\bm\omega_3)$, is
+\begin{equation}\begin{array}{r@{\ }>{\displaystyle}l}
+H_K=&H_0+V_0+V_h=:H_0+V\\[0.3cm]
+H_0=&\sum_{\alpha\in\{\uparrow,\downarrow\}}\sum_{x=-{L}/2}^{{L}/2-1} c^+_\alpha(x)\,\left(-\frac{\Delta}2-1\right)\,c^-_\alpha(x)\\[0.5cm]
+V_0=&-\lambda_0\sum_{j=1,2,3\atop\alpha_1,\alpha_2} c^+_{\alpha_1}(0)\sigma^j_{\alpha_1,\alpha_2}c^-_{\alpha_2}(0)\, \tau^j\\[0.5cm]
+V_h=&-h \,\sum_{j=1,2,3}\bm\omega_j \tau^j
+\end{array}\label{eqhamdef}\end{equation} 
+where $\lambda_0$ is the interaction strength, $\Delta$ is the discrete Laplacian $c_\alpha^\pm(x),\,\alpha=\uparrow,\downarrow$ are creation and annihilation operators acting on {\it electrons}, and $\sigma^j=\tau^j,\,j=1,2,3$, are Pauli matrices. The operators $\tau^j$ act on the {\it impurity}. The boundary conditions are taken to be periodic.\par
+
+\indent In the {\it Andrei model} [\cite{andEZ}], the impurity is represented by a fermion instead of a two-level system, that is the Hilbert space is replaced by $\mathcal F_L\otimes\mathcal F_1$, and the Hamiltonian is defined by replacing $\tau^j$ in~(\ref{eqhamdef}) by $d^+\tau^jd^-$ in which $d_\alpha^\pm(x),\,\alpha=\uparrow,\downarrow$ are creation and annihilation operators acting on the impurity.\par
+\bigskip
+
+\indent The partition function $Z={\rm Tr}\, e^{-\beta H_K}$ can be expressed formally as a functional integral:
+\begin{equation}
+Z=\mathrm{Tr}\int P(d\psi)\, \sum_{n=0}^\infty(-1)^n\int_{0<t_1<\cdots<t_n<\beta}\kern-50pt dt_1\cdots dt_n\, \mathcal V(t_1)\cdots\mathcal V(t_n)
+\label{eqpartfn}\end{equation}
+in which $\mathcal V(t)$ is obtained from $V$ by replacing $c_\alpha^\pm(0)$ in~(\ref{eqhamdef}) by a {\it Grassmann} field $\psi_\alpha^\pm(0,t)$, $P(d\psi)$ is a {\it Gaussian Grassmann measure} over the fields $\{\psi_\alpha^\pm(0,t)\}_{t,\alpha}$ whose {\it propagator} ({\it i.e.} {\it covariance}) is, in the $L\to\infty$ limit,
+$$
+g(t,t')=\frac1{(2\pi)^2}\int dk dk_0 \frac{e^{i k_0(t-t')}}{i k_0-\cos k},
+$$
+and the trace is over the state-space of the spin-1/2 impurity, that is a trace over $\mathbb C^2$.\par
+\bigskip
+
+\indent We will consider a {\it hierarchical} version of the $s-d$ model. The hierarchical model defined below is {\it inspired} by the $s-d$ model in the same way as the hierarchical model defined in [\cite{bgjOFi}] was inspired by the Andrei model. We will not give any details on the justification of the definition, as such considerations are entirely analogous to the discussion in [\cite{bgjOFi}].\par
+
+\indent The model is defined by introducing a family of {\it hierarchical fields} and specifying a {\it propagator} for each pair of fields. The average of any monomial of fields is then computed using the Wick rule.\par
+
+\indent Assuming $\beta=2^{N_\beta}$ with $N_\beta=\log_2\beta\in\mathbb N$, the time axis $[0,\beta)$ is paved with boxes ({\it i.e.} intervals) of size $2^{-m}$ for every $m\in\{0,-1,\ldots,-N_\beta\}$: let 
+\begin{equation}
+\mathcal Q_m:=\left\{[i 2^{|m|}, (i+1) 2^{|m|})\right\}_{i=0,1,\cdots,2^{N_\beta-|m|}-1}^{m=0,-1,\ldots}
+\label{eqtiledef}\end{equation}
+Given a box $\Delta\in{\mathcal Q}_m$, let $t_\Delta$ denote the center of $\Delta$, and given a point $t\in R$, let $\Delta^{[m]}(t)$ be the (unique) box on scale $m$ that contains $t$. We further decompose each box $\Delta\in\mathcal Q_m$ into two {\it half boxes}: for $\eta\in\{-,+\}$, let 
+\begin{equation}
+\Delta_{\eta}:=\Delta^{[m+1]}(t_{\Delta}+\eta2^{-m-2})
+\label{eqhalfboxdef}\end{equation} 
+for $m\le 0$. Thus $\Delta_{-}$ can be called the ``lower half'' of $\Delta$ and $\Delta_{+}$ the ``upper half''.\par
+
+\indent The elementary fields used to define the hierarchical $s-d$ model will be {\it constant on each half-box} and will be denoted by $\psi_\alpha^{[m]\pm}(\Delta_{\eta})$ for $m\in\{0,-1,\cdots,$ $-N_\beta\}$, $\Delta\in\mathcal Q_m$, $\eta\in\{-,+\}$, $\alpha\in\{\uparrow,\downarrow\}$.\par
+
+\indent The propagator of the hierarchical $s-d$ model is defined as 
+\begin{equation}
+\left<\psi_{\alpha}^{[m]-}(\Delta_{-\eta})\psi_{\alpha}^{[m]+}(\Delta_{\eta})\right >:= \eta
+\label{eqprop}\end{equation} 
+for $m\in\{0,-1,\cdots,$ $-N_\beta\}$, $\Delta\in\mathcal Q_m$, $\eta\in\{-,+\}$, $\alpha\in\{\uparrow,\downarrow\}$. The propagator of any other pair of fields is set to 0.\par
+
+\indent Finally, we define 
+\begin{equation}
+\psi^\pm_\alpha(t):= \sum_{m=0}^{-N_\beta} 2^{\frac{m}2}\psi_\alpha^{[m]\pm}(\Delta^{[m+1]}(t)).
+\label{eqfielddcmp}\end{equation} 
+
+\indent The partition function for the hierarchical $s-d$ model is 
+\begin{equation}
+Z=\mathrm{Tr}\left< \sum_{n=0}^\infty(-1)^n\int_{0<t_1<\cdots<t_n<\beta}\kern-50pt dt_1\cdots dt_n\, \mathcal V(t_1)\cdots\mathcal V(t_n) \right>
+\label{eqhierpartfn}\end{equation} 
+in which the $\psi^\pm_\alpha(0,t)$ in $\mathcal V(t)$ have been replaced by the $\psi_\alpha^\pm(t)$ defined in~(\ref{eqfielddcmp}): 
+\begin{equation}
+\mathcal V(t):=-\lambda_0\sum_{j=1,2,3\atop\alpha_1,\alpha_2} \psi^+_{\alpha_1}(t)\sigma^j_{\alpha_1,\alpha_2}\psi^-_{\alpha_2}(t)\, \tau^j -h \,\sum_{j=1,2,3}\bm\omega_j \tau^j.
+\label{eqhierpot}\end{equation} 
+This concludes the definition of the hierarchical $s-d$ model.\par
+\bigskip
+
+
+\indent We will now show how to compute the partition function~(\ref{eqhierpartfn}) using a renormalization group iteration. We first rewrite 
+\begin{equation}
+\sum_{n=0}^\infty(-1)^n\int_{0<t_1<\cdots<t_n<\beta}\kern-50pt dt_1\cdots dt_n\, \mathcal V(t_1)\cdots\mathcal V(t_n) =\prod_{\Delta\in\mathcal Q_0}\prod_{\eta=\pm}\left(\sum_{n=0}^\infty\frac{(-1)^n}{2^nn!}\mathcal V(t_{\Delta_\eta})^n\right)
+\label{eqtrotthier}\end{equation} 
+and find that 
+\begin{equation}
+\sum_{n=0}^\infty\frac{(-1)^n}{2^nn!}\mathcal V(t_{\Delta_\eta^{[0]}})^n =C\left(1+\sum_{p}\ell_p^{[0]}O_{p,\eta}^{[\le 0]}(\Delta^{[0]})\right)
+\label{eqexpV}\end{equation} 
+with 
+\begin{equation}\begin{array}{r@{\quad}l}
+O_{0,\eta}^{[\le 0]}(\Delta):=\frac12\mathbf A^{[\le 0]}_\eta(\Delta)\cdot\bm\tau,& O_{1,\eta}^{[\le 0]}(\Delta):=\frac12\mathbf A^{[\le 0]}_\eta(\Delta)^2,\\[0.3cm]
+O_{4,\eta}^{[\le 0]}(\Delta):=\frac12\mathbf A^{[\le 0]}_\eta(\Delta)\cdot\bm\omega,& O_{5,\eta}^{[\le 0]}(\Delta):=\frac12\mathbf \bm\tau\cdot\bm\omega,\\[0.3cm]
+O_{6,\eta}^{[\le 0]}(\Delta):=\frac12(\mathbf A^{[\le 0]}_\eta(\Delta)\cdot\bm\omega)(\bm\tau\cdot\bm\omega),& O_{7,\eta}^{[\le 0]}(\Delta):=\frac12(\mathbf A^{[\le 0]}_\eta(\Delta)^2)(\bm\tau\cdot\bm\omega)
+\end{array}\label{eqOdef}\end{equation} 
+(the numbering is meant to recall that in [\cite{bgjOFi}]) in which $\bm\tau=(\tau^1,\tau^2,\tau^3)$ and $\mathbf A_\eta^{[\le 0]}(\Delta)$ is a vector of polynomials in the fields whose $j$-th component for $j\in\{1,2,3\}$ is 
+\begin{equation}
+A_\eta^{[\le 0]j}(\Delta):=\sum_{(\alpha,\alpha')\in\{\uparrow,\downarrow\}^2} \psi_\alpha^{[\le 0]+}(\Delta_\eta)\sigma^j_{\alpha,\alpha'}\psi_{\alpha'}^{[\le 0]-}(\Delta_\eta)
+\label{eqAdef}\end{equation} 
+$\psi_\alpha^{[\le 0]\pm}:=\sum_{m\le0}2^{\frac m2}\psi_\alpha^{[m]\pm}$, and 
+\begin{equation}\begin{array}{r@{\ }>{\displaystyle}l}
+C=&\cosh(\tilde h),\quad \ell_0^{[0]}=\frac1C\frac{\lambda_0}{\tilde h}\sinh(\tilde h),\quad
+\ell_1^{[0]}=\frac1C\frac{\lambda_0^2}{12\tilde h}(\tilde h\cosh(\tilde h)+2\sinh(\tilde h))\\[0.3cm]
+\ell_4^{[0]}=&\frac1C\lambda_0\sinh(\tilde h),\quad \ell_5^{[0]}=\frac1C\sinh(\tilde h),\quad
+\ell_6^{[0]}=\frac1C\frac{\lambda_0}{\tilde h}(\tilde h\cosh(\tilde h)-\sinh(\tilde h))\\[0.3cm]
+\ell_7^{[0]}=&\frac1C\frac{\lambda_0^2}{12\tilde h^2}(\tilde h^2\sinh(\tilde h)+2\tilde h\cosh(\tilde h)-2\sinh(\tilde h))
+\end{array}\label{eqinitcd}\end{equation} 
+in which $\tilde h:=h/2$.\par
+
+\indent By a straightforward induction, we find that the partition function~(\ref{eqhierpartfn}) can be computed by defining 
+\begin{equation}
+C^{[m]}\mathcal W^{[m-1]}(\Delta^{[m]}):=\left<\prod_\eta\left(\mathcal W^{[m]}(\Delta^{[m]}_\eta)\right)\right>_m
+\label{eqindW}\end{equation} 
+in which $\left<\cdot\right>_m$ denotes the average over $\psi^{[m]}$, $C^{[m]}>0$ and 
+\begin{equation}
+\mathcal W^{[m-1]}(\Delta^{[m]})=1+\sum_p\ell_p^{[m]}O_p^{[\le m]}(\Delta^{[m]})
+\label{eqexprW}\end{equation} 
+in terms of which 
+\begin{equation}
+Z=C^{2|\mathcal Q_0|}\prod_{m=-N(\beta)+1}^0(C^{[m]})^{|\mathcal Q_{m-1}|}
+\label{eqZind}\end{equation} 
+in which $|\mathcal Q_m|=2^{N(\beta)-|m|}$ is the cardinality of $\mathcal Q_m$. In addition, similarly to [\cite{bgjOFi}], the map relating $\ell_p^{[m]}$ to $\ell_p^{[m-1]}$ and $C^{[m]}$ can be computed explicitly from~(\ref{eqindW}):
+\begin{equation}\begin{array}{r@{\ }>{\displaystyle}l}
+C^{[m]} =& 1 +\frac{3}{2}\ell_{0}^2 +\ell_{0}\ell_{6} +9\ell_{1}^2 +\frac{\ell_{4}^2}{2} +\frac{\ell_{5}^2}{4} +\frac{\ell_{6}^2}{2} +9\ell_{7}^2 \\[0.3cm]
+\ell^{[m-1]}_{0} =& \frac1C\left(\ell_{0} -\ell_{0}^2 +3\ell_{0}\ell_{1} -\ell_{0}\ell_{6} \right)\\[0.3cm]
+\ell^{[m-1]}_{1} =& \frac1C\left(\frac{\ell_{1}}{2} +\frac{\ell_{0}^2}{8} +\frac{\ell_{0}\ell_{6}}{12} +\frac{\ell_{4}^2}{24} +\frac{\ell_{5}\ell_{7}}{4} +\frac{\ell_{6}^2}{24} \right)\\[0.3cm]
+\ell^{[m-1]}_{4} =& \frac1C\left(\ell_{4} +\frac{\ell_{0}\ell_{5}}{2} +3\ell_{0}\ell_{7} +3\ell_{1}\ell_{4} +\frac{\ell_{5}\ell_{6}}{2} +3\ell_{6}\ell_{7} \right)\\[0.3cm]
+\ell^{[m-1]}_{5} =& \frac1C\left(2\ell_{5} +2\ell_{0}\ell_{4} +36\ell_{1}\ell_{7} +2\ell_{4}\ell_{6} \right)\\[0.3cm]
+\ell^{[m-1]}_{6} =& \frac1C\left(\ell_{6} +\ell_{0}\ell_{6} +3\ell_{1}\ell_{6} +\frac{\ell_{4}\ell_{5}}{2} +3\ell_{4}\ell_{7} \right)\\[0.3cm]
+\ell^{[m-1]}_{7} =& \frac1C\left(\frac{\ell_{7}}{2} +\frac{\ell_{0}\ell_{4}}{12} +\frac{\ell_{1}\ell_{5}}{4} +\frac{\ell_{4}\ell_{6}}{12} \right)
+\end{array}\label{eqbetafun}\end{equation}
+in which the $^{[m]}$ have been dropped from the right hand side.\par
+\bigskip
+
+
+\indent The flow equation~(\ref{eqbetafun}) can be recovered from that of the hierarchical Andrei model studied in [\cite{bgjOFi}] (see in particular [\cite{bgjOFi}, (C1)] by restricting the flow to the invariant submanifold defined by \begin{equation} \ell_2^{[m]}=\frac13,\quad \ell_3^{[m]}=\frac16\ell_1^{[m]},\quad \ell_8^{[m]}=\frac16\ell_4^{[m]}. \label{e18}\end{equation} This is of particular interest since $\ell_2^{[m]}$ is a relevant coupling and the fact that it plays no role in the $s-d$ model indicates that it has little to no physical relevance.\par
+
+\indent The qualitative behavior of the flow is therefore the same as that described in [\cite{bgjOFi}] for the hierarchical Andrei model. In particular the susceptibility, which can be computed by deriving $-\beta^{-1}\log Z$ with respect to $h$, remains finite in the 0-temperature limit as long as $\lambda_0<0$, that is as long as the interaction is anti-ferromagnetic.\par
+\hugeskip
+
+{\bf Acknowledgements}: We are grateful to G.~Benfatto for many enlightening discussions on the $s-d$ and Andrei's models.
+
+\hugeskip
+
+\small
+\BBlography
+
+\vfill
+\eject
+
+\end{document}
diff --git a/README b/README
new file mode 100644
index 0000000..50e5582
--- /dev/null
+++ b/README
@@ -0,0 +1,49 @@
+* Typeset
+
+In order to typeset the LaTeX document, run
+  pdflatex Gallavotti_Jauslin_2015.tex
+  pdflatex Gallavotti_Jauslin_2015.tex
+
+
+* Files
+
+  Gallavotti_Jauslin_2015.tex :
+    body of the paper.
+
+  bibliography.BBlog.tex :
+    list of references.
+
+  BBlog.sty :
+    bibliography related commands.
+
+  header.sty :
+    list of packages.
+
+  iansecs.sty :
+    main style file.
+
+  kiss.cls :
+    barebones class file
+
+  toolbox.sty :
+    collection of useful commands.
+
+
+* Coding style
+
+In the body of the paper, an effort has been made to keep the LaTeX code
+'standard', avoiding self-defined commands whenever possible, and sticking to
+TeX and basic LaTeX commands. In some instances however, such an approach would
+have been too restrictive, and commands defined in the style files listed above
+were used.
+
+Many of the commands defined in 'iansecs.sty' are drop-in replacements for
+standard LaTeX commands, though some functionality may be lost.
+
+
+* Bibliography
+
+The bibliography was generated by BBlog, which produced the
+bibliography.BBlog.tex file. All of the required code to adequately typeset
+the reference list and define the commands used to cite them are contained in
+that file.
diff --git a/bibliography.BBlog.tex b/bibliography.BBlog.tex
new file mode 100644
index 0000000..67a19e0
--- /dev/null
+++ b/bibliography.BBlog.tex
@@ -0,0 +1,20 @@
+\hrefanchor
+\outdef{citeandSO}{And61}
+\hbox{\parbox[t]{\rw}{[\cite{andSO}]}\parbox[t]{\colw}{P.~Anderson - {\it Localized magnetic states in metals}, Physical Review, Vol.~124, n.~1, p.~41-53, 1961.}}\par
+\bigskip
+
+\hrefanchor
+\outdef{citeandEZ}{And80}
+\hbox{\parbox[t]{\rw}{[\cite{andEZ}]}\parbox[t]{\colw}{N.~Andrei - {\it Diagonalization of the Kondo Hamiltonian}, Physical Review Letters, Vol.~45, n.~5, 1980.}}\par
+\bigskip
+
+\hrefanchor
+\outdef{citebgjOFi}{BGJ15}
+\hbox{\parbox[t]{\rw}{[\cite{bgjOFi}]}\parbox[t]{\colw}{G.~Benfatto, G.~Gallavotti, I.~Jauslin - {\it Kondo effect in a Fermionic hierarchical model}, arXiv 1506.04381, 2015.}}\par
+\bigskip
+
+\hrefanchor
+\outdef{citekonSF}{Kon64}
+\hbox{\parbox[t]{\rw}{[\cite{konSF}]}\parbox[t]{\colw}{J.~Kondo - {\it Resistance minimum in dilute magnetic alloys}, Progress of Theoretical Physics, Vol.~32, n.~1, 1964.}}\par
+\bigskip
+
diff --git a/header.sty b/header.sty
new file mode 100644
index 0000000..b8492a9
--- /dev/null
+++ b/header.sty
@@ -0,0 +1,11 @@
+%%
+%% Load packages
+%%
+
+\usepackage{color}
+\usepackage[hidelinks]{hyperref}
+\usepackage{amsfonts}
+\usepackage{bm}
+\usepackage{array}
+\usepackage{etoolbox}
+
diff --git a/iansecs.sty b/iansecs.sty
new file mode 100644
index 0000000..ee6ab04
--- /dev/null
+++ b/iansecs.sty
@@ -0,0 +1,402 @@
+%%
+%% This file contains the main style commands
+%%
+%% Some options can be set by changing the \loaddefaults command
+%%
+
+\usepackage{color}
+\usepackage{marginnote}
+
+\def\loaddefaults{
+  \sectionsfalse
+  \subseqcountfalse
+  \def\seqskip{\vskip1.5cm}
+  \def\subseqskip{\vskip1cm}
+  \resetpointattheofalse
+  \parindent=0pt
+  \def\indent{\hskip20pt}
+}
+
+% false if there are no sections
+\newif\ifsections
+% true if equation numbers should include the subsection number
+\newif\ifsubseqcount
+% true if there is a table of contents
+\newif\iftoc
+% true if point counting should reset at each theorem
+\newif\ifresetpointattheo
+
+% a prefix to put before the section number, e.g. A for appendices
+\def\sectionprefix{}
+
+\loaddefaults
+
+%% style for the equation number
+\def\eqnumstyle{}
+
+%% correct vertical alignment at the end of a document
+\AtEndDocument{
+  \vfill
+  \eject
+}
+
+%% hyperlinks
+% hyperlinkcounter
+\newcounter{lncount}
+% hyperref anchor
+\def\hrefanchor{%
+\stepcounter{lncount}%
+\hypertarget{ln.\thelncount}{}%
+}
+
+%% define a command and write it to aux file
+\def\outdef#1#2{%
+% define command
+\expandafter\xdef\csname #1\endcsname{#2}%
+% hyperlink number
+\expandafter\xdef\csname #1@hl\endcsname{\thelncount}%
+% write command to aux
+\immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1\endcsname{\csname #1\endcsname}}%
+\immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1@hl\endcsname{\thelncount}}%
+}
+
+
+%% define a label for the latest tag
+%% label defines a command containing the string stored in \tag
+\AtBeginDocument{
+  \def\label#1{\expandafter\outdef{#1}{\safe\tag}}
+
+\def\ref#1{%
+% check whether the label is defined (hyperlink runs into errors if this check is ommitted)
+\ifcsname #1@hl\endcsname%
+\hyperlink{ln.\csname #1@hl\endcsname}{\safe\csname #1\endcsname}%
+\else%
+\ifcsname #1\endcsname%
+\csname #1\endcsname%
+\else%
+{\bf ??}%
+\fi%
+\fi%
+}
+}
+
+%% counters
+\newcounter{sectioncount}
+\newcounter{subsectioncount}
+\newcounter{pointcount}
+\newcounter{subpointcount}
+\newcounter{subsubpointcount}
+\newcounter{seqcount}
+\newcounter{figcount}
+\newcounter{Theocount}
+\newcounter{tocsectioncount}
+\newcounter{tocsubsectioncount}
+
+%% section command
+\newlength\secnumwidth
+\newlength\sectitlewidth
+\def\section#1{%
+% reset counters
+\stepcounter{sectioncount}%
+\setcounter{subsectioncount}{0}%
+\setcounter{pointcount}{0}%
+\setcounter{subpointcount}{0}%
+\setcounter{subsubpointcount}{0}%
+\setcounter{figcount}{0}%
+\setcounter{Theocount}{0}%
+\setcounter{seqcount}{0}%
+% space before section (if not first)
+\ifnum\thesectioncount>1%
+\seqskip%
+\penalty-1000%
+\fi%
+% hyperref anchor
+\hrefanchor%
+% define tag (for \label)
+\xdef\tag{\sectionprefix\thesectioncount}%
+% get widths
+\def\@secnum{{\bf\Large\sectionprefix\thesectioncount.\hskip10pt}}%
+\settowidth\secnumwidth{\@secnum}%
+\setlength\sectitlewidth\textwidth%
+\addtolength\sectitlewidth{-\secnumwidth}%
+% print name
+\parbox{\textwidth}{%
+\@secnum%
+\parbox[t]{\sectitlewidth}{\Large\bf #1}}%
+% write to table of contents
+\iftoc%
+% save lncount in aux variable which is written to toc
+\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@sec.\thesectioncount\endcsname{\thelncount}}%
+\write\tocoutput{\noexpand\tocsection{#1}{\thepage}}%
+\fi%
+\par\penalty10000%
+\bigskip\penalty10000%
+}
+
+%% subsection
+\def\subsection#1{
+% counters
+\stepcounter{subsectioncount}%
+\setcounter{pointcount}{0}%
+\setcounter{subpointcount}{0}%
+\setcounter{subsubpointcount}{0}%
+\ifsubseqcount%
+\setcounter{seqcount}0%
+\fi%
+% space before subsection (if not first)
+\ifnum\thesubsectioncount>1%
+\subseqskip%
+\penalty-500%
+\fi%
+% hyperref anchor
+\hrefanchor
+% define tag (for \label)
+\xdef\tag{\sectionprefix\thesectioncount.\thesubsectioncount}%
+% get widths
+\def\@secnum{{\bf\large\hskip.5cm\sectionprefix\thesectioncount.\thesubsectioncount.\hskip5pt}}%
+\settowidth\secnumwidth{\@secnum}%
+\setlength\sectitlewidth\textwidth%
+\addtolength\sectitlewidth{-\secnumwidth}%
+% print name
+\parbox{\textwidth}{%
+\@secnum%
+\parbox[t]{\sectitlewidth}{\large\bf #1}}%
+% write to table of contents
+\iftoc%
+% save lncount in aux variable which is written to toc
+\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@subsec.\thesectioncount.\thesubsectioncount\endcsname{\thelncount}}%
+\write\tocoutput{\noexpand\tocsubsection{#1}{\thepage}}%
+\fi%
+\par\penalty10000%
+\medskip\penalty10000%
+}
+
+%% itemize
+\newlength\itemizeskip
+% left margin for items
+\setlength\itemizeskip{20pt}
+% item symbol
+\def\itemizept{\textbullet}
+\newlength\itemizeseparator
+% space between the item symbol and the text
+\setlength\itemizeseparator{5pt}
+
+\newlength\current@itemizeskip
+\setlength\current@itemizeskip{0pt}
+\def\itemize{
+  \par\medskip
+  \addtolength\current@itemizeskip{\itemizeskip}
+  \leftskip\current@itemizeskip
+}
+\def\enditemize{
+  \addtolength\current@itemizeskip{-\itemizeskip}
+  \par\leftskip\current@itemizeskip
+  \medskip
+}
+\newlength\itempt@total
+\def\item{
+  \settowidth\itempt@total{\itemizept}
+  \addtolength\itempt@total{\itemizeseparator}
+  \par
+  \medskip
+  \hskip-\itempt@total\itemizept\hskip\itemizeseparator
+}
+
+%% points
+\def\point{
+  \stepcounter{pointcount}
+  \setcounter{subpointcount}{0}
+  % hyperref anchor
+  \hrefanchor
+  \indent{\bf \thepointcount\ - }
+  % define tag (for \label)
+  \xdef\tag{\thepointcount}
+}
+\def\subpoint{
+  \stepcounter{subpointcount}
+  \setcounter{subsubpointcount}0
+  % hyperref anchor
+  \hrefanchor
+  \indent\hskip.5cm{\bf \thepointcount-\thesubpointcount\ - }
+  % define tag (for \label)
+  \xdef\tag{\thepointcount-\thesubpointcount}
+}
+\def\subsubpoint{
+  \stepcounter{subsubpointcount}
+  % hyperref anchor
+  \hrefanchor
+  \indent\hskip1cm{\bf \thepointcount-\thesubpointcount-\thesubsubpointcount\ - }
+  % define tag (for \label)
+  \xdef\tag{\thepointcount-\thesubpointcount-\thesubsubpointcount}
+}
+% reset points
+\def\resetpointcounter{
+  \setcounter{pointcount}{0}
+  \setcounter{subpointcount}{0}
+  \setcounter{subsubpointcount}{0}
+}
+
+%% equation numbering
+\def\seqcount{
+  \stepcounter{seqcount}
+  % the output
+  \edef\seqformat{\theseqcount}
+  % add subsection number
+  \ifsubseqcount
+    \let\tmp\seqformat
+    \edef\seqformat{\thesubsectioncount.\tmp}
+  \fi
+  % add section number
+  \ifsections
+    \let\tmp\seqformat
+    \edef\seqformat{\sectionprefix\thesectioncount.\tmp}
+  \fi
+  % define tag (for \label)
+  \xdef\tag{\seqformat}
+  % write number
+  \marginnote{\eqnumstyle\hfill(\seqformat)}
+}
+%% equation environment compatibility
+\def\equation{\hrefanchor$$\seqcount}
+\def\endequation{$$\@ignoretrue}
+
+%% figures
+\newlength\figwidth
+\setlength\figwidth\textwidth
+\addtolength\figwidth{-2.5cm}
+
+\def\figcount#1{%
+\stepcounter{figcount}%
+% hyperref anchor
+\hrefanchor%
+% the number of the figure
+\edef\figformat{\thefigcount}%
+% add section number
+\ifsections%
+\let\tmp\figformat%
+\edef\figformat{\sectionprefix\thesectioncount.\tmp}%
+\fi%
+% define tag (for \label)
+\xdef\tag{\figformat}%
+% write
+\hfil fig \figformat: \parbox[t]{\figwidth}{\small#1}%
+\par\bigskip%
+}
+
+%% environment
+\def\figure{
+  \par\penalty-500
+}
+\def\endfigure{
+  \par\penalty-1000
+}
+\let\caption\figcount
+
+%% delimiters
+\def\delimtitle#1{\par \leavevmode\raise.3em\hbox to\hsize{\lower0.3em\hbox{\vrule height0.3em}\hrulefill\ \lower.3em\hbox{#1}\ \hrulefill\lower0.3em\hbox{\vrule height0.3em}}\par\penalty10000}
+\def\delim{\par\leavevmode\raise.3em\hbox to\hsize{\vrule height0.3em\hrulefill\vrule height0.3em}\par\penalty10000}
+\def\enddelim{\par\penalty10000\leavevmode\raise.3em\hbox to\hsize{\vrule height0.3em\hrulefill\vrule height0.3em}\par}
+
+%% theorem headers
+\def\theo#1{
+  \stepcounter{Theocount}
+  % reset points
+  \ifresetpointattheo\resetpointcounter\fi
+  % hyperref anchor
+  \hrefanchor
+  % the number
+  \def\formattheo{\theTheocount}
+  % add section number
+  \ifsections
+    \let\tmp\formattheo
+    \edef\formattheo{\sectionprefix\thesectioncount.\tmp}
+  \fi
+  % define tag (for \label)
+  \xdef\tag{\formattheo}
+  % write
+  \delimtitle{\bf #1 \formattheo}
+}
+\let\endtheo\enddelim
+
+%% start appendices
+\def\appendix{%
+\vfill
+\pagebreak
+% counter
+\setcounter{sectioncount}0%
+% prefix
+\def\sectionprefix{A}%
+% write
+{\bf \LARGE Appendices}\par\penalty10000\bigskip\penalty10000%
+% add a mention in the table of contents
+\iftoc%
+\immediate\write\tocoutput{\noexpand\tocappendices}\penalty10000%
+\fi%
+%% uncomment for new page for each appendix
+%\def\seqskip{\vfill\pagebreak}
+}
+
+%% start references
+\def\references{%
+\hrefanchor%
+% write
+{\bf \LARGE References}\par\penalty10000\bigskip\penalty10000%
+% add a mention in the table of contents
+\iftoc%
+% save lncount in aux variable which is written to toc
+\immediate\write\tocoutput{\noexpand\expandafter\noexpand\edef\noexpand\csname toc@references\endcsname{\thelncount}}%
+\write\tocoutput{\noexpand\tocreferences{\thepage}}\penalty10000%
+\fi%
+}
+
+
+%% table of contents
+\newif\iftocopen
+\def\tableofcontents{
+{\bf \large Table of contents:}\par\penalty10000\bigskip\penalty10000%
+% copy content from file
+\IfFileExists{\jobname.toc}{\input{\jobname.toc}}{{\tt error: table of contents missing}}
+% open new toc
+\newwrite\tocoutput
+\immediate\openout\tocoutput=\jobname.toc
+\toctrue
+}
+%% close file
+\AtEndDocument{
+  % close toc
+  \iftoc
+    \immediate\closeout\tocoutput
+  \fi
+}
+
+
+%% fill line with dots
+\def\leaderfill{\leaders\hbox to 1em {\hss. \hss}\hfill}
+
+%% same as sectionprefix
+\def\tocsectionprefix{}
+
+%% toc formats
+\def\tocsection #1#2{
+  \stepcounter{tocsectioncount}
+  \setcounter{tocsubsectioncount}{0}
+  % write
+  \smallskip\hyperlink{ln.\csname toc@sec.\thetocsectioncount\endcsname}{{\bf \tocsectionprefix\thetocsectioncount}.\hskip5pt #1\leaderfill#2}\par
+}
+\def\tocsubsection #1#2{
+  \stepcounter{tocsubsectioncount}
+  % write
+  {\hskip10pt\hyperlink{ln.\csname toc@subsec.\thetocsectioncount.\thetocsubsectioncount\endcsname}{{\bf \thetocsubsectioncount}.\hskip5pt {\small #1}\leaderfill#2}}\par
+}
+\def\tocappendices{
+  \medskip
+  \setcounter{tocsectioncount}0
+  {\bf Appendices}\par
+  \smallskip
+  \def\tocsectionprefix{A}
+}
+\def\tocreferences#1{
+  \medskip
+  {\hyperlink{ln.\csname toc@references\endcsname}{{\bf References}\leaderfill#1}}\par
+  \smallskip
+}
diff --git a/kiss.cls b/kiss.cls
new file mode 100644
index 0000000..51d36b8
--- /dev/null
+++ b/kiss.cls
@@ -0,0 +1,42 @@
+%%
+%% Barebones class declaration
+%%
+
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+\ProvidesClass{kiss}
+
+\setlength\paperheight {297mm}
+\setlength\paperwidth  {210mm}
+
+%% fonts
+\input{size11.clo}
+\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
+\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
+\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
+\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
+\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
+\DeclareOldFontCommand{\sl}{\normalfont\slshape}{\@nomath\sl}
+\DeclareOldFontCommand{\sc}{\normalfont\scshape}{\@nomath\sc}
+
+%% something is wrong with \thepage, redefine it
+\gdef\thepage{\the\c@page}
+
+%% default offsets: 1in, correct with \hoffset and \voffset
+\hoffset=-50pt
+\voffset=-72pt
+%% horizontal margins
+%\oddsidemargin=31pt
+%\evensidemargin=31pt
+%% vertical margin
+%\topmargin=20pt
+%% body size
+\textwidth=460pt
+\textheight=704pt
+%% header size and margin
+%\headheight=12pt
+%\headsep=25pt
+%% footer size
+%\footskip=30pt
+%% margin size and margin
+\marginparwidth=35pt
+%\marginparsep=10pt
diff --git a/toolbox.sty b/toolbox.sty
new file mode 100644
index 0000000..620ed50
--- /dev/null
+++ b/toolbox.sty
@@ -0,0 +1,41 @@
+%%
+%% A collection of useful commands
+%%
+
+%% can call commands even when they are not defined
+\def\safe#1{%
+\ifdefined#1%
+#1%
+\else%
+{\color{red}\bf?}%
+\fi%
+}
+
+
+%% larger skip
+\newskip\hugeskipamount
+  \hugeskipamount=24pt plus8pt minus8pt
+\def\hugeskip{\vskip\hugeskipamount}
+
+
+%% penalty before large blocks
+\def\preblock{
+  \penalty-500
+}
+
+%% listparpenalty prevents page breaks before lists
+\newcount\prevparpenalty
+\def\listparpenalty{
+  \prevparpenalty=\@beginparpenalty
+  \@beginparpenalty=10000
+}
+%% back to previous value
+\def\unlistparpenalty{
+  \@beginparpenalty=\prevparpenalty
+}
+
+
+%% array spanning the entire line
+\def\largearray{\begin{array}{@{}>{\displaystyle}l@{}}\hphantom{\hspace{\textwidth}}\\[-.5cm]}
+\def\endlargearray{\end{array}}
+
-- 
cgit v1.2.3-54-g00ecf