From 3862267129d8b61224161eb3d163b83e1833cf87 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Sun, 10 Jul 2022 19:51:14 +0200
Subject: New figures.

---
 frsb_kac-rice.tex | 28 ++++++++++++++++++----------
 1 file changed, 18 insertions(+), 10 deletions(-)

(limited to 'frsb_kac-rice.tex')

diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex
index a1ac0c1..130b7e9 100644
--- a/frsb_kac-rice.tex
+++ b/frsb_kac-rice.tex
@@ -887,8 +887,7 @@ become dominant over minima at a higher energy $E_\mathrm{th}=-1.287\,575\,114\l
 The 1RSB complexity transitions to a RS description for dominant stationary points at an energy
 $E_1=-1.273\,886\,852\ldots$. The highest energy for which the 1RSB description exists is $E_\mathrm{max}=-0.886\,029\,051\ldots$
 
-All these complexities can be seen plotted in
-Fig.~\ref{fig:2rsb.complexity}.
+The complexity along interesting trajectories is plotted in Fig.~\ref{fig:2rsb.complexity}.
 
 
 
@@ -907,9 +906,11 @@ Fig.~\ref{fig:2rsb.complexity}.
 
 \begin{figure}
   \centering
+  \hspace{-1em}
   \includegraphics{figs/316_complexity_contour_1.pdf}
+  \hspace{-1em}
   \includegraphics{figs/316_complexity_contour_2.pdf}
-  \raisebox{4em}{\includegraphics{figs/316_complexity_contour_leg.pdf}}
+  \raisebox{3em}{\includegraphics{figs/316_complexity_contour_leg.pdf}}
 
   \caption{
     Complexity of the $3+16$ model in the energy $E$ and stability $\mu$
@@ -927,13 +928,20 @@ Fig.~\ref{fig:2rsb.complexity}.
   \includegraphics{figs/316_detail.pdf}
 
   \caption{
-    Complexity of the $3+16$ model in the energy $E$ and stability $\mu$
-    plane. The right shows a detail of the left. The black line shows $\mu_m$,
-    which separates minima above from saddles below. The white lines show the
-    dominant stationary points at each energy, dashed when they are described
-    by a RS solution and solid for 1RSB. The red line shows the transition
-    between RS and 1RSB descriptions. The gray line shows where the RS
-    description predicts zero complexity.
+    Detail of the `phases' of the $3+16$ model complexity as a function of
+    energy and stability. Above the yellow marginal stability line the
+    complexity counts saddles of fixed index, while below that line it counts
+    minima of fixed stability. The shaded red region shows places where the
+    complexity is described by the 1RSB solution, while the shaded gray region
+    shows places where the complexity is described by the RS solution. In white
+    regions the complexity is zero. Several interesting energies are marked
+    with vertical black lines: the traditional `threshold' $E_\mathrm{th}$
+    where minima become most numerous, the algorithmic threshold
+    $E_\mathrm{alg}$ that bounds the performance of smooth algorithms, and the
+    average energies at the $2$RSB and $1$RSB equilibrium transitions $\langle
+    E\rangle_2$ and $\langle E\rangle_1$, respectively. Though the figure is
+    suggestive, $E_\mathrm{alg}$ lies slightly below the termination of the RS
+    -- 1RSB transition line.
   }
 \end{figure}
 
-- 
cgit v1.2.3-70-g09d2

