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Diffstat (limited to 'topology.tex')
| -rw-r--r-- | topology.tex | 6 |
1 files changed, 3 insertions, 3 deletions
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 |