From 29b1b91c174103c1f6536ec4db72cbaef67f0576 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Fri, 7 Feb 2025 20:35:20 -0300
Subject: Fixed typo in relationship between V₀ and E.
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The role of N in the relationship was inverted at the beginning of
section 3.
---
 topology.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'topology.tex')

diff --git a/topology.tex b/topology.tex
index 965df01..9000b12 100644
--- a/topology.tex
+++ b/topology.tex
@@ -632,9 +632,9 @@ into the structure of solutions in this regime is merited.
 \label{sec:ssg}
 
 When $M=1$ the solution manifold corresponds to the energy
-level set of a spherical spin glass with energy density $E=\sqrt NV_0$. All the
+level set of a spherical spin glass with energy density $E=V_0/\sqrt N$. All the
 results from the previous sections follow, and can be translated to the spin
-glasses by taking the limit $\alpha\to0$ while keeping $E=V_0\alpha^{-1/2}$ fixed. With a little algebra this procedure yields
+glasses by taking the limit $\alpha\to0$ while keeping $E=V_0\alpha^{1/2}$ fixed. With a little algebra this procedure yields
 \begin{align}
   E_\text{on}=\pm\sqrt{2f(1)}
   &&
@@ -642,7 +642,7 @@ glasses by taking the limit $\alpha\to0$ while keeping $E=V_0\alpha^{-1/2}$ fixe
   \label{eq:ssg.energies}
 \end{align}
 for the onset and shattering energies. The same limit taken for
-$V_\text{\textsc{sat}}\alpha^{-1/2}$ coincides with the ground state energy
+$V_\text{\textsc{sat}}\alpha^{1/2}$ coincides with the ground state energy
 $E_\text{gs}$. In fact, for all energies below the threshold energy
 $E_\text{th}$ (where minima become more numerous than saddle points in the
 spin glass energy function) the logarithm of the average Euler characteristic
-- 
cgit v1.2.3-70-g09d2

