From 48adc92f4bb460663109ff04072c45b0f7a58963 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Fri, 28 Jun 2019 15:05:05 -0400
Subject: added comment on consistency given the big ginzburg critereon

---
 main.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'main.tex')

diff --git a/main.tex b/main.tex
index 4264884..fb73629 100644
--- a/main.tex
+++ b/main.tex
@@ -263,7 +263,7 @@ For large argument, $\mathcal I(x)\sim x^{-4}$, yielding
 \begin{equation}
   t_\G^{9/4}\sim\frac{2k_B}{\pi\Delta c_V\xi_{\parallel0}^2\xi_{\perp0}^5q_*^4}
 \end{equation}
-Experiments give $\Delta c_V\simeq1\times10^5\,\J\,\m^{-3}\,\K^{-1}$ \cite{fisher_specific_1990}, and our fit above gives $\xi_{\perp0}q_*=(D_\perp q_*^4/aT_c)^{1/4}\sim2$. We have reason to believe that at zero pressure, very far from the Lifshitz point, $q_*$ is roughly the inverse lattice spacing \textbf{[Why???]}. Further supposing that $\xi_{\parallel0}\simeq\xi_{\perp0}$, we find $t_\G\sim0.04$, so that an experiment would need to be within $\sim1\,\K$ to detect a deviation from mean field behavior. An ultrasound experiment able to capture data over several decades within this vicinity of $T_c$ may be able to measure a cusp with $|t|^\gamma$ for $\gamma=\text{\textbf{???}}$, the empirical exponent \textbf{[Citation???]}.
+Experiments give $\Delta c_V\simeq1\times10^5\,\J\,\m^{-3}\,\K^{-1}$ \cite{fisher_specific_1990}, and our fit above gives $\xi_{\perp0}q_*=(D_\perp q_*^4/aT_c)^{1/4}\sim2$. We have reason to believe that at zero pressure, very far from the Lifshitz point, $q_*$ is roughly the inverse lattice spacing \textbf{[Why???]}. Further supposing that $\xi_{\parallel0}\simeq\xi_{\perp0}$, we find $t_\G\sim0.04$, so that an experiment would need to be within $\sim1\,\K$ to detect a deviation from mean field behavior. An ultrasound experiment able to capture data over several decades within this vicinity of $T_c$ may be able to measure a cusp with $|t|^\gamma$ for $\gamma=\text{\textbf{???}}$, the empirical exponent \textbf{[Citation???]}. Our analysis has looked at behavior for $T-T_c>1\,\K$, and so it remains self-consistent.
 
 \begin{acknowledgements}
 
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