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| author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2021-10-25 11:30:14 +0200 |
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| committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2021-10-25 11:30:14 +0200 |
| commit | b441490981ec0a3262e9e5acef85ddf899d885a9 (patch) | |
| tree | 8cd789a6378854e531a180ebd8b160af293f8384 | |
| parent | da1ed12ac1ebd0c538400734fc0c6b88f4769265 (diff) | |
| download | paper-b441490981ec0a3262e9e5acef85ddf899d885a9.tar.gz paper-b441490981ec0a3262e9e5acef85ddf899d885a9.tar.bz2 paper-b441490981ec0a3262e9e5acef85ddf899d885a9.zip | |
Added note about singular free energy.
| -rw-r--r-- | ising_scaling.tex | 9 |
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) |