From a30cca363958cd8bb4de480432b791a3711614a4 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 10 Dec 2020 15:25:18 +0100
Subject: Nudging Figure 1 around to minimize blank space...

---
 bezout.tex | 45 ++++++++++++++++++++++-----------------------
 1 file changed, 22 insertions(+), 23 deletions(-)

diff --git a/bezout.tex b/bezout.tex
index 949a55b..bfabdec 100644
--- a/bezout.tex
+++ b/bezout.tex
@@ -228,29 +228,6 @@ z$, or alternatively the magnitude $y^2$ of the imaginary part. The latter
 vanishes as $a\to1$, where we should recover known results for the real
 $p$-spin.
 
-\begin{figure}[htpb]
-  \centering
-
-  \includegraphics{fig/spectra_0.0.pdf}
-  \includegraphics{fig/spectra_0.5.pdf}\\
-  \includegraphics{fig/spectra_1.0.pdf}
-  \includegraphics{fig/spectra_1.5.pdf}
-
-  \caption{
-    Eigenvalue and singular value spectra of the matrix $\partial\partial H$
-    for $p=3$, $a=\frac54$, and $\kappa=\frac34e^{-i3\pi/4}$ with (a)
-    $\epsilon=0$, (b) $\epsilon=-\frac12|\epsilon_{\mathrm{th}}|$, (c)
-    $\epsilon=-|\epsilon_{\mathrm{th}}|$, and (d)
-    $\epsilon=-\frac32|\epsilon_{\mathrm{th}}|$. The shaded region of each inset
-    shows the support of the eigenvalue distribution. The solid line on each
-    plot shows the distribution of singular values, while the overlaid
-    histogram shows the empirical distribution from $2^{10}\times2^{10}$ complex
-    normal matrices with the same covariance and diagonal shift as
-    $\partial\partial H$.
-  } \label{fig:spectra}
-\end{figure}
-
-
 The Hessian of \eqref{eq:constrained.hamiltonian} is $\partial\partial
 H=\partial\partial H_0-p\epsilon I$, or the Hessian of
 \eqref{eq:bare.hamiltonian} with a constant added to its diagonal. The
@@ -285,6 +262,28 @@ knowledge a closed form is not in the literature.  We have worked out an implici
 this spectrum using the saddle point of a replica symmetric calculation for the
 Green function.
 
+\begin{figure}[htpb]
+  \centering
+
+  \includegraphics{fig/spectra_0.0.pdf}
+  \includegraphics{fig/spectra_0.5.pdf}\\
+  \includegraphics{fig/spectra_1.0.pdf}
+  \includegraphics{fig/spectra_1.5.pdf}
+
+  \caption{
+    Eigenvalue and singular value spectra of the matrix $\partial\partial H$
+    for $p=3$, $a=\frac54$, and $\kappa=\frac34e^{-i3\pi/4}$ with (a)
+    $\epsilon=0$, (b) $\epsilon=-\frac12|\epsilon_{\mathrm{th}}|$, (c)
+    $\epsilon=-|\epsilon_{\mathrm{th}}|$, and (d)
+    $\epsilon=-\frac32|\epsilon_{\mathrm{th}}|$. The shaded region of each inset
+    shows the support of the eigenvalue distribution. The solid line on each
+    plot shows the distribution of singular values, while the overlaid
+    histogram shows the empirical distribution from $2^{10}\times2^{10}$ complex
+    normal matrices with the same covariance and diagonal shift as
+    $\partial\partial H$.
+  } \label{fig:spectra}
+\end{figure}
+
 Introducing replicas to bring the partition function to
 the numerator of the Green function \cite{Livan_2018_Introduction} gives
 \begin{widetext}
-- 
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