From e2edf2e648b2f5f4fc95250a992e7085c7c2c33e Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 5 Aug 2019 22:01:42 -0400
Subject: scalar vector component pedantry

---
 main.tex | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/main.tex b/main.tex
index a194abd..094e3a4 100644
--- a/main.tex
+++ b/main.tex
@@ -213,7 +213,7 @@ with $r\to\tilde r=r-b^2/4\lambda_\X$.
 
 With the strain traced out \eqref{eq:fo} describes the theory of a Lifshitz
 point at $\tilde r=c_\perp=0$ \cite{lifshitz_theory_1942,
-lifshitz_theory_1942-1}. For a scalar order parameter ($\Bog$ or $\Btg$) it is
+lifshitz_theory_1942-1}. For a one-component order parameter ($\Bog$ or $\Btg$) it is
 traditional to make the field ansatz $\eta(x)=\eta_*\cos(q_*x_3)$. For $\tilde
 r>0$ and $c_\perp>0$, or $\tilde r<c_\perp^2/4D_\perp$ and $c_\perp<0$, the
 only stable solution is $\eta_*=q_*=0$ and the system is unordered. For $\tilde
@@ -226,9 +226,9 @@ $q_*^2=-c_\perp/2D_\perp$ and
     =\frac{\tilde r_c-\tilde r}{3u}
 \end{equation}
 with $\tilde r_c=c_\perp^2/4D_\perp$ and the system has modulated order. The
-transition between the uniform and modulated orderings is abrupt for a scalar
+transition between the uniform and modulated orderings is abrupt for a one-component
 field and occurs along the line $c_\perp=-2\sqrt{-D_\perp\tilde r/5}$. For a
-vector order parameter ($\Eg$) we must also allow a relative phase between the
+two-component order parameter ($\Eg$) we must also allow a relative phase between the
 two components of the field. In this case the uniform ordered phase is only
 stable for $c_\perp>0$, and the modulated phase is now characterized by helical
 order with $\eta(x)=\eta_*\{\cos(q_*x_3),\sin(q_*x_3)\}$ and
@@ -249,9 +249,9 @@ diagrams for this model are shown in Figure \ref{fig:phases}.
   \caption{
     Phase diagrams for (a) \urusi\ from experiments (neglecting the
     superconducting phase) \cite{hassinger_temperature-pressure_2008} (b) mean
-    field theory of a scalar ($\Bog$ or $\Btg$) Lifshitz point (c) mean field
-    theory of a vector ($\Eg$) Lifshitz point. Solid lines denote continuous
-    transitions, while dashed lines denote abrupt transitions.
+    field theory of a one-component ($\Bog$ or $\Btg$) Lifshitz point (c) mean
+    field theory of a two-component ($\Eg$) Lifshitz point. Solid lines denote
+    continuous transitions, while dashed lines denote abrupt transitions.
   }
   \label{fig:phases}
 \end{figure}
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