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| author | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2023-08-23 15:55:52 +0200 |
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| committer | Jaron Kent-Dobias <jaron@kent-dobias.com> | 2023-08-23 23:34:47 +0200 |
| commit | b8a0e53bfaca590fb6f7aa4f14a4f69630c6ff9c (patch) | |
| tree | 909a8fe3e6baefe61eebe79ac85fc39ce512e687 /when_annealed.tex | |
| parent | 4a9455031004be737f10a1a1a786a3de79c623fa (diff) | |
| download | EPL_143_61003-b8a0e53bfaca590fb6f7aa4f14a4f69630c6ff9c.tar.gz EPL_143_61003-b8a0e53bfaca590fb6f7aa4f14a4f69630c6ff9c.tar.bz2 EPL_143_61003-b8a0e53bfaca590fb6f7aa4f14a4f69630c6ff9c.zip | |
Fixed some references at the request of a reviewer.
Diffstat (limited to 'when_annealed.tex')
| -rw-r--r-- | when_annealed.tex | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/when_annealed.tex b/when_annealed.tex index c24f2c4..282ebc4 100644 --- a/when_annealed.tex +++ b/when_annealed.tex @@ -74,7 +74,7 @@ without much reflection \cite{Wainrib_2013_Topological, Kent-Dobias_2021_Complex Gershenzon_2023_On-Site}. In a few cases researchers have instead made the better-controlled quenched average, which averages the logarithm of the number of stationary points, and find deviations from the annealed approximation with -important implications for behavior \cite{Muller_2006_Marginal, +important implications for behavior \cite{Cavagna_1999_Quenched, Crisanti_2006_Spherical, Muller_2006_Marginal, Ros_2019_Complex, Kent-Dobias_2023_How, Ros_2023_Quenched, Ros_2023_Generalized}. Generically, the annealed approximation to the complexity is wrong when a nonvanishing fraction of pairs of stationary points have nontrivial correlations in their @@ -125,7 +125,7 @@ Crisanti_2011_Statistical, BenArous_2019_Geometry, Subag_2020_Following, ElAlaou There are several well-established results on the equilibrium of this model. First, if the function $\chi(q)=f''(q)^{-1/2}$ is convex then it is not possible for the equilibrium solution to have nontrivial correlations between states at any -temperature \cite{Crisanti_1992_The}.\footnote{ +temperature \cite{Crisanti_2006_Spherical, Crisanti_2007_Amorphous-amorphous}.\footnote{ More specifically, convex $\chi$ cannot have an equilibrium order with more than {\oldstylenums1\textsc{rsb}} order among the configurations. In equilibrium, {\oldstylenums1\textsc{rsb}} corresponds to trivial correlations between |