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Ian Jauslin 2015-10-19 14:10:46 +00:00
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Giuliani_Jauslin_2015.tex
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@ -233,7 +233,7 @@ in which $\gamma_4$ and $\Delta$ are negligible, and the Fermi surface is approx
\par
\bigskip
{\bf Remark:} If $\gamma_4=\Delta0$, then the error term $O(\epsilon^{4}\|\mathbf k'_{j}\|_{\mathrm{III}}^{-1})$ in (\ref{freeschwinth}) vanishes identically, which allows us to extend the third regime to all momenta satisfying
{\bf Remark:} If $\gamma_4=\Delta=0$, then the error term $O(\epsilon^{4}\|\mathbf k'_{j}\|_{\mathrm{III}}^{-1})$ in (\ref{freeschwinth}) vanishes identically, which allows us to extend the third regime to all momenta satisfying
$$\|\mathbf k'_{j}\|_{\mathrm{III}}\ll\epsilon^3.$$
@ -505,7 +505,7 @@ and complete the proofs of the Main Theorem, as well as of Theorems \ref{theoo},
\section{The model}
\label{themodelsec}
\hfil\framebox{\bf From this point on, we set $\gamma_4=\Delta0$.}
\hfil\framebox{\bf From this point on, we set $\gamma_4=\Delta=0$.}
\bigskip
\indent In this section, we define the model in precise terms, re-express the free energy and two-point Schwinger function in terms of Grassmann integrals and truncated expectations, which we will subsequently explain how to compute, and discuss the symmetries of the model and their representation in this formalism.\par