Update on Overleaf.

1 files changed, 1 insertions, 1 deletions

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,