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| -rw-r--r-- | frsb_kac-rice.tex | 2 |
1 files changed, 1 insertions, 1 deletions
diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex index 6f1945d..d513e48 100644 --- a/frsb_kac-rice.tex +++ b/frsb_kac-rice.tex @@ -913,7 +913,7 @@ 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, |