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| -rw-r--r-- | main.tex | 11 |
1 files changed, 6 insertions, 5 deletions
@@ -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] |