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| -rw-r--r-- | when_annealed.tex | 6 |
1 files changed, 3 insertions, 3 deletions
diff --git a/when_annealed.tex b/when_annealed.tex index 37ee7fb..512ff12 100644 --- a/when_annealed.tex +++ b/when_annealed.tex @@ -41,7 +41,7 @@ counts are reliably found by taking the average of the logarithm (the quenched average), which is more difficult and not often done in practice. When most stationary points are uncorrelated with each other, quenched and - anneals averages are equal. Equilibrium heuristics can guarantee when most of + annealed averages are equal. Equilibrium heuristics can guarantee when most of the lowest minima will be uncorrelated. We show that these equilibrium heuristics cannot be used to draw conclusions about other minima and saddles by producing examples among Gaussian-correlated functions on the hypersphere @@ -369,7 +369,7 @@ $e$, $g$, and $h$ are given by transition, coincides with it in this case. The gray shaded region highlights the minima, which are stationary points with $\mu\geq\mu_\mathrm m$. $E_\textrm{min}$ is marked on the plot as the lowest energy at which - extensive saddles are found. + saddles of extensive index are found. } \label{fig:complexity_35} \end{figure} @@ -457,7 +457,7 @@ of saddles $E_\mathrm{min}$. Also, these models have a transition boundary that smoothly connects $E_{\oldstylenums1\textsc{rsb}}^+$ and $E_{\oldstylenums1\textsc{rsb}}^-$, so $E_{\oldstylenums1\textsc{rsb}}^-$ corresponds to the lower bound of \textsc{rsb} complexity. For large enough -$s$, the range passes into minima, which is excepted as these models have +$s$, the range passes into minima, which is expected as these models have nontrivial complexity of their ground states. This also seems to correspond with the decoupling of the \textsc{rsb} solutions connected to $E_{\oldstylenums1\textsc{rsb}}^+$ and $E_{\oldstylenums1\textsc{rsb}}^-$, with |