From 216a7e6e5a83f11a35cb0003657f30590a7781bd Mon Sep 17 00:00:00 2001 From: Jaron Kent-Dobias Date: Wed, 25 Sep 2019 15:09:58 -0400 Subject: Rewording OP free energy paragraph. --- main.tex | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/main.tex b/main.tex index 9e1e41a..67b8ef3 100644 --- a/main.tex +++ b/main.tex @@ -179,10 +179,11 @@ on \op\ symmetries that can produce linear couplings to strain. Looking at the components present in \eqref{eq:strain-components}, this rules out all of the u-reps (which are odd under inversion) and the $\Atg$ irrep. -If the \op\ transforms like $\Aog$, odd terms are allowed in its -free energy and any transition will be abrupt and not continuous without -fine-tuning. For $\X$ as any of $\Bog$, $\Btg$, or $\Eg$, the most general quadratic -free energy density is +If the \op\ transforms like $\Aog$, odd terms are allowed in its free energy +and any transition will be abrupt and not continuous without fine-tuning. Since +this is not a feature of \urusi\ \ho\ physics, we will henceforth rule it out +as well. For $\X$ as any of $\Bog$, $\Btg$, or $\Eg$, the most general +quadratic free energy density is \begin{equation} \begin{aligned} f_\op=\frac12\big[&r\eta^2+c_\parallel(\nabla_\parallel\eta)^2 @@ -195,7 +196,7 @@ where $\nabla_\parallel=\{\partial_1,\partial_2\}$ transforms like $\Eu$ and $\nabla_\perp=\partial_3$ transforms like $\Atu$. Other quartic terms are allowed---especially many for an $\Eg$ \op---but we have included only those terms necessary for stability when either $r$ or $c_\perp$ become negative. The -full free energy functional of $\eta$ and $\epsilon$ is then +full free energy functional of $\eta$ and $\epsilon$ is \begin{equation} \begin{aligned} F[\eta,\epsilon] -- cgit v1.2.3-70-g09d2