From b441490981ec0a3262e9e5acef85ddf899d885a9 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
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(-)

(limited to 'ising_scaling.tex')

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 v1.2.3-54-g00ecf

