From ddc18664974154798ab4c865589f90cd60d20264 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Wed, 21 Aug 2019 15:06:30 -0400
Subject: added comments on irreps

---
 main.tex | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

(limited to 'main.tex')

diff --git a/main.tex b/main.tex
index 0a31ff4..a245429 100644
--- a/main.tex
+++ b/main.tex
@@ -155,6 +155,7 @@ action of the point group, or
     \epsilon_\Btg^{(1)}=2\epsilon_{12}               \\
     \epsilon_\Eg^{(1)}=2\{\epsilon_{11},\epsilon_{22}\}.
   \end{aligned}
+  \label{eq:strain-components}
 \end{equation}
 Next, all quadratic combinations of these irreducible strains that transform
 like $\Aog$ are included in the free energy as
@@ -183,7 +184,7 @@ If $\X$ is a representation not present in the strain there can be no linear
 coupling, and the effect of $\eta$ going through a continuous phase transition
 is to produce a jump in the $\Aog$ strain stiffness. We will therefore focus
 our attention on order parameter symmetries that produce linear couplings to
-strain.
+strain. Looking at the components present in \eqref{eq:strain-components}, this rules out all of the u-reps (odd under inversion) and the $\Atg$ irrep as having any anticipatory response in the strain stiffness.
 
 If the order parameter transforms like $\Aog$, odd terms are allowed in its
 free energy and any transition will be abrupt and not continuous without
-- 
cgit v1.2.3-70-g09d2

