From 1d62111c843740b89c80fd2f1dbd0a70925cf7a3 Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Wed, 6 May 2020 20:06:06 -0400 Subject: Updated some citekeys. --- main.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) (limited to 'main.tex') diff --git a/main.tex b/main.tex index 3da57a9..374519e 100644 --- a/main.tex +++ b/main.tex @@ -286,7 +286,7 @@ to $f_\op$ with the identification $r\to\tilde r=r-b^2/2C^0_\X$. \end{figure} With the strain traced out, \eqref{eq:fo} describes the theory of a Lifshitz -point at $\tilde r=c_\perp=0$.\cite{Lifshitz_1942a, Lifshitz_1942b} The +point at $\tilde r=c_\perp=0$.\cite{Lifshitz_1942_OnI, Lifshitz_1942_OnII} The properties discussed in the remainder of this section can all be found in a standard text, e.g., in chapter 4 \S6.5 of Chaikin \& Lubensky.\cite{Chaikin_1995} For a one-component \op\ ($\Bog$ or $\Btg$) and @@ -579,7 +579,7 @@ thermodynamic phase transition). Three dimensions is below the upper critical dimension $4\frac12$ of a one-component disordered-to-modulated transition, and so mean field theory should break down sufficiently close to the critical point due to fluctuations, -at the Ginzburg temperature. \cite{Hornreich_1980, Ginzburg_1961} Magnetic +at the Ginzburg temperature. \cite{Hornreich_1980, Ginzburg_1961_Some} Magnetic phase transitions tend to have a Ginzburg temperature of order one. Our fit above gives $\xi_{\perp0}q_*=(D_\perp q_*^4/aT_c)^{1/4}\simeq2$, which combined with the speculation of $q_*\simeq\pi/a_3$ puts the bare correlation length @@ -589,7 +589,7 @@ mean field exponent suggests that this region is outside the Ginzburg region, but an experiment may begin to see deviations from mean field behavior within approximately several Kelvin of the critical point. An ultrasound experiment with more precise temperature resolution near the critical point may be able to -resolve a modified cusp exponent $\gamma\simeq1.31$,\cite{Guida_1998} since the +resolve a modified cusp exponent $\gamma\simeq1.31$,\cite{Guida_1998_Critical} since the universality class of a uniaxial modulated one-component \op\ is $\mathrm O(2)$.\cite{Garel_1976} We should not expect any quantitative agreement between mean field theory and experiment in the low temperature phase since, by the -- cgit v1.2.3-70-g09d2