<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">From 6df867fda7aa0b0a42ef1933615ef0b40ff50209 Mon Sep 17 00:00:00 2001
From: "kurchan.jorge" &lt;kurchan.jorge@gmail.com&gt;
Date: Wed, 6 Jul 2022 14:01:10 +0000
Subject: Update on Overleaf.

---
 frsb_kac-rice.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'frsb_kac-rice.tex')

diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex
index 9fc4b34..04cac67 100644
--- a/frsb_kac-rice.tex
+++ b/frsb_kac-rice.tex
@@ -842,7 +842,7 @@ The complexities are
 The maximum is given by $\Sigma_1'=\Sigma_2'=\hat \beta$, provided it occurs in the phase
 in which both $\Sigma_1$ and $\Sigma_2$ are non-zero. The two systems are `thermalized',
 and it is easy to see that, because many points contribute, the overlap between two 
-global configurations $$\frac1 {2N}({\mathbf s^1},{\mathbf \sigma^1})\cdot ({\mathbf s^2},{\mathbf \sigma^2})=0$$ This is the `annealed' phase of a Kac-Rice calculation.
+global configurations $$\frac1 {2N}({\mathbf s^1},{\mathbf \sigma^1})\cdot ({\mathbf s^2},{\mathbf \sigma^2})=\frac1 {2N}[ {\mathbf s^1}\cdot {\mathbf s^2}+ {\mathbf \sigma^1}\cdot {\mathbf \sigma^2}] =0$$ This is the `annealed' phase of a Kac-Rice calculation.
 
 Now start going down in energy, or up in $\hat \beta$: there will be a point $e_c$, $\hat \beta_c$
 at which one of the subsystems freezes at its lower energy density, say it is system one,
-- 
cgit v1.2.3-70-g09d2

</pre></body></html>