From 242a8e123d473e1f255288e0f03dcbb608d907fc Mon Sep 17 00:00:00 2001
From: Ian Jauslin <ian.jauslin@roma1.infn.it>
Date: Sun, 11 Sep 2016 22:39:42 +0000
Subject: Small change in the abstract, and the conclusion.

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 Giuliani_Jauslin_2015.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'Giuliani_Jauslin_2015.tex')

diff --git a/Giuliani_Jauslin_2015.tex b/Giuliani_Jauslin_2015.tex
index 139b864..fd45555 100644
--- a/Giuliani_Jauslin_2015.tex
+++ b/Giuliani_Jauslin_2015.tex
@@ -23,7 +23,7 @@
 
 \hugeskip
 
-\indent We consider a model of half-filled bilayer graphene, in which the three dominant Slonczewski-Weiss-McClure hopping parameters are retained, in the presence of short range interactions. Under a smallness assumption on the interaction strength $U$ as well as on the inter-layer hopping $\epsilon$, we construct the ground state in the thermodynamic limit, and prove its analyticity in $U$, uniformly in $\epsilon$. The interacting Fermi surface is degenerate, and consists of eight Fermi points, two of which are protected by symmetries, while the locations of the other six are renormalized by the interaction, and the effective dispersion relation at the Fermi points is conical.  The construction reveals the presence of different energy regimes, where the effective behavior of correlation functions changes qualitatively. The analysis of the crossover between regimes plays an important role in the proof of analyticity and in the uniform control of the radius of convergence.  The proof is based on a rigorous implementation of fermionic renormalization group methods, including determinant estimates for the renormalized expansion.\par
+\indent We consider a model of half-filled bilayer graphene, in which the three dominant Slonczewski-Weiss-McClure hopping parameters are retained, in the presence of short range interactions. Under a smallness assumption on the interaction strength $U$ as well as on the inter-layer hopping $\epsilon$, we construct the ground state in the thermodynamic limit, and prove that the pressure and two point Schwinger function, away from its singularities, are analytic in $U$, uniformly in $\epsilon$. The interacting Fermi surface is degenerate, and consists of eight Fermi points, two of which are protected by symmetries, while the locations of the other six are renormalized by the interaction, and the effective dispersion relation at the Fermi points is conical.  The construction reveals the presence of different energy regimes, where the effective behavior of correlation functions changes qualitatively. The analysis of the crossover between regimes plays an important role in the proof of analyticity and in the uniform control of the radius of convergence.  The proof is based on a rigorous implementation of fermionic renormalization group methods, including determinant estimates for the renormalized expansion.\par
 
 \hugeskip
 
@@ -76,7 +76,7 @@ at least in the case we are treating, namely small interaction strength and smal
 
 \indent The transition from a normal phase to one with broken symmetry as the interaction strength is increased from small to intermediate values was studied in~[\cite{CTV12}] at second order in perturbation theory. Therein, it was found that while at small bare couplings the infrared flow is convergent, at larger couplings it tends to increase, indicating a transition towards an {\it electronic nematic state}.\par
 
-\indent Let us also mention that the third regime is not believed to give an adequate description of the system at arbitrarily small energies: at energies smaller than a third threshold (proportional to the fourth power of the transverse hopping) one finds~[\cite{PP06}] that the six extra Fermi points around the two original ones, are actually microscopic ellipses. The analysis of the thermodynamic properties of the system in this regime (to be called the fourth regime) requires new ideas and techniques, due to the extended nature of the singularity, and goes beyond the scope of this paper. It may be possible to adapt the ideas of~[\cite{BGM06}] to this regime, and we hope to come back to this issue in a future publication. 
+\indent Let us also mention that the third regime is not believed to give an adequate description of the system at arbitrarily small energies: at energies smaller than a third threshold (proportional to the fourth power of the transverse hopping) one finds~[\cite{PP06}] that the six extra Fermi points around the two original ones, are actually microscopic ellipses. The analysis of the thermodynamic properties of the system in this regime (to be called the fourth regime) requires new ideas and techniques, due to the extended nature of the singularity, and goes beyond the scope of this paper. It may be possible to adapt the ideas of~[\cite{BGM06}] to this regime, which would allow us to carry out the analysis down to temperatures that are exponentially low in the coupling constant, and we hope to come back to this issue in a future publication.
 \par
 \bigskip
 
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