From f88291534ace74aba7d8b75e12bcea1ccda7e6e4 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Fri, 8 Jul 2022 18:39:15 +0200
Subject: Style tweaks.

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

(limited to 'frsb_kac-rice.tex')

diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex
index 51c72bf..913a77e 100644
--- a/frsb_kac-rice.tex
+++ b/frsb_kac-rice.tex
@@ -837,7 +837,7 @@ With this covariance, the model sees a replica symmetric to 1RSB transition at
 $\beta_1=1.70615\ldots$ and a 1RSB to 2RSB transition at
 $\beta_2=6.02198\ldots$. At these transitions, the average energies are
 $\langle E\rangle_1=-0.906391\ldots$ and $\langle E\rangle_2=-1.19553\ldots$,
-respectively, and the ground state energy is $E_0=-1.2876055305\ldots$.
+respectively, and the ground state energy is $E_0=-1.287\,605\,530\ldots$.
 Besides these typical equilibrium energies, an energy of special interest for
 looking at the landscape topology is the \emph{algorithmic threshold}
 $E_\mathrm{alg}$, defined by the lowest energy reached by local algorithms like
@@ -852,7 +852,7 @@ ground state energy. For the pure $p$-spin models,
 $E_\mathrm{alg}=E_\mathrm{th}$, where $E_\mathrm{th}$ is the energy at which
 marginal minima are the most common stationary points. Something about the
 topology of the energy function is relevant to where this algorithmic threshold
-lies. For the $3+16$ model at hand, $E_\mathrm{alg}=1.275140128\ldots$.
+lies. For the $3+16$ model at hand, $E_\mathrm{alg}=-1.275\,140\,128\ldots$.
 
 In this model, the RS complexity gives an inconsistent answer for the
 complexity of the ground state, predicting that the complexity of minima
@@ -860,10 +860,10 @@ vanishes at a higher energy than the complexity of saddles, with both at a
 lower energy than the equilibrium ground state. The 1RSB complexity resolves
 these problems, predicting the same ground state as equilibrium and that the
 complexity of marginal minima (and therefore all saddles) vanishes at
-$E_m=-1.2876055265\ldots$, which is very slightly greater than $E_0$. Saddles
-become dominant over minima at a higher energy $E_s=-1.287605716\ldots$.
+$E_m=-1.287\,605\,527\ldots$, which is very slightly greater than $E_0$. Saddles
+become dominant over minima at a higher energy $E_\mathrm{th}=-1.287\,605\,716\ldots$.
 Finally, the 1RSB complexity transitions to a RS description at an energy
-$E_1=-1.27135996\ldots$. All these complexities can be seen plotted in
+$E_1=-1.271\,359\,96\ldots$. All these complexities can be seen plotted in
 Fig.~\ref{fig:2rsb.complexity}.
 
 All of the landmark energies associated with the complexity are a great deal
@@ -891,7 +891,7 @@ E\rangle_2$.
   \includegraphics{figs/316_complexity_contour_2.pdf}
 
   \caption{
-    Complexity of the $3+16$ model in the energy $E$ and radial reaction $\mu$
+    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
-- 
cgit v1.2.3-70-g09d2

