From d0d0103960c8d5c606abb994b7d78c6df0f1204e Mon Sep 17 00:00:00 2001 From: Ian Jauslin Date: Sun, 11 Sep 2016 23:55:47 +0000 Subject: Update to v1.1 Add references: [MW67] and [MW73] Typos --- Giuliani_Jauslin_Lieb_2015.tex | 7 ++++--- bibliography.BBlog.tex | 2 ++ 2 files changed, 6 insertions(+), 3 deletions(-) diff --git a/Giuliani_Jauslin_Lieb_2015.tex b/Giuliani_Jauslin_Lieb_2015.tex index e539376..4744ccc 100644 --- a/Giuliani_Jauslin_Lieb_2015.tex +++ b/Giuliani_Jauslin_Lieb_2015.tex @@ -77,8 +77,9 @@ diagonalized as in [\cite{Li67}]. The partition function can then be computed by if it is a finite portion of a lattice) they decay polynomially at large distances, like $1/(distance)$, asymptotically as the size of the graph tends to infinity. See [\cite{PR08}] for a proof of this fact on the square lattice on the half-plane. +A similar analysis has been worked out in the 2D nearest neighbor Ising model for the boundary free energy, in the presence of a boundary magnetic field, and for the boundary spin-spin correlations, see [\cite{MW67}, Section 8] and [\cite{MW73}, Chapters VI and VII]. If the graph is a discrete, regular, approximation of a finite domain of $\mathbb R^2$, -the scaling limit of these correlations +the scaling limit of the boundary monomer correlations at close-packing is expected to exist and to be conformally invariant under conformal mappings of the domain, in analogy with other observables of the critical 2D Ising model and of the close-packed dimer model [\cite{Ke00}, \cite{Ke01}, \cite{Sm01}, \cite{Sm10}, \cite{CHI15}, \cite{Du11}, \cite{Du15}]. In particular, they are expected to coincide with those of complex chiral free fermions [\cite{PR08}]. @@ -180,7 +181,7 @@ M_n(i_1,\cdots,i_{2n})=\mathrm{pf}(\mathfrak M_{i_1,\ldots,i_{2n}}), where $\mathfrak M_{i_1,\ldots,i_{2n}}$ is the $2n\times 2n$ antisymmetric matrix whose $(j,j')$-th entry with $j