From 0a73432fb5e4dedb4cac14e9722fe8a26aa69e1a Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Tue, 17 Sep 2019 13:34:24 -0400
Subject: defining some variables now that the ginzburg paragraph has been
 removed

---
 main.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'main.tex')

diff --git a/main.tex b/main.tex
index 98266fc..af39f7f 100644
--- a/main.tex
+++ b/main.tex
@@ -302,8 +302,8 @@ Near the unordered--modulated transition this yields
   \end{aligned}
   \label{eq:susceptibility}
 \end{equation}
-with $\xi_\perp=(|\Delta\tilde r|/D_\perp)^{-1/4}$ and
-$\xi_\parallel=(|\Delta\tilde r|/c_\parallel)^{-1/2}$. We must emphasize that
+with $\xi_\perp=(|\Delta\tilde r|/D_\perp)^{-1/4}=\xi_{\perp0}|t|^{-1/4}$ and
+$\xi_\parallel=(|\Delta\tilde r|/c_\parallel)^{-1/2}=\xi_{\parallel0}|t|^{-1/2}$, where $t=(T-T_c)/T_c$ is the reduced temperature and $\xi_{\perp0}=(D_\perp/aT_c)^{1/4}$ and $\xi_{\parallel0}=(c_\parallel/aT_c)^{1/2}$ are the bare correlation lengths. We must emphasize that
 this is \emph{not} the magnetic susceptibility because a $\Bog$ or $\Btg$ \op\
 cannot couple linearly to a uniform magnetic field. The object defined in
 \eqref{eq:sus_def} is most readily interpreted as proportional to the two-point
@@ -442,7 +442,7 @@ $q_*$ should continuously vanish. Far from the Lifshitz point we expect the
 wavevector to lock into values commensurate with the space group of the
 lattice, and moreover that at zero pressure, where the \rus\ data here was
 collected, the half-wavelength of the modulation should be commensurate with
-the lattice, or $q_*\simeq0.328\,\A^{-1}$ \cite{meng_imaging_2013,
+the lattice spacing $a_3\simeq9.68\,\A$, or $q_*=\pi/a_3\simeq0.328\,\A^{-1}$ \cite{meng_imaging_2013,
 broholm_magnetic_1991, wiebe_gapped_2007, bourdarot_precise_2010}. In between
 these two regimes, the ordering wavevector should shrink by jumping between
 ever-closer commensurate values in the style of the devil's staircase
-- 
cgit v1.2.3-70-g09d2

