From b441490981ec0a3262e9e5acef85ddf899d885a9 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Mon, 25 Oct 2021 11:30:14 +0200 Subject: Added note about singular free energy. --- ising_scaling.tex | 9 +++++++-- 1 file changed, 7 insertions(+), 2 deletions(-) diff --git a/ising_scaling.tex b/ising_scaling.tex index c7e7adb..32085ab 100644 --- a/ising_scaling.tex +++ b/ising_scaling.tex @@ -120,8 +120,13 @@ which are exact as written \cite{Raju_2019_Normal}. The flow of the free energy is linearized as nearly as possible. The quadratic term in that equation is unremovable due to a resonance between the value of $\nu$ and the spatial dimension in two dimensions, while its coefficient is chosen as a -matter of convention, fixing the scale of $u_t$. Solving these equations for -$u_f$ yields +matter of convention, fixing the scale of $u_t$. The form $u_f$ of the free +energy is known as the singular part of the free energy, since it is equivalent +to subtracting an analytic function of the control variables from the free +energy, breaking it into pieces that scale homogenously and inhomogenously with +renormalization. + +Solving these equations for $u_f$ yields \begin{equation} \begin{aligned} u_f(u_t, u_h) -- cgit v1.2.3-70-g09d2