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1 files 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)