New writing in first figure caption.

1 files changed, 5 insertions, 1 deletions

diff --git a/stokes.tex b/stokes.tex
index 8b89104..095f6cb 100644
--- a/stokes.tex
+++ b/stokes.tex
@@ -161,7 +161,11 @@ action potentially has more stationary points. We'll call $\Sigma$ the set of
     its complex extension. \textbf{Right:} The stationary points of $\mathcal
     S$ in the complex-$\theta$ plane. In this example,
     $\Sigma=\{\blacklozenge,\bigstar,\blacktriangle,\blacktriangledown,\bullet,\blacksquare\}$
-    and $\Sigma_0=\{\blacklozenge,\blacktriangledown\}$.
+    and $\Sigma_0=\{\blacklozenge,\blacktriangledown\}$. Symmetries exist
+    between the stationary points both as a result of the conjugation symmetry
+    of $\mathcal S$, which produces the vertical reflection, and because in the
+    pure 3-spin models $\mathcal S(-s)=-\mathcal S(s)$, which produces the
+    simultaneous translation and inversion symmetry.
   }
 \end{figure}