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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 15:55:52 +0200 |
commit | cf86b2620a6a5e06f2f2b028722b34c17bf54792 (patch) | |
tree | 5b317e12fe43541321d5639625d24a86fe8c59fd /when_annealed.tex | |
parent | 1ed47199fd34bbeed29f2d0d0d5c420bb4e67c0b (diff) | |
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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 0bbaf51..ae14616 100644 --- a/when_annealed.tex +++ b/when_annealed.tex @@ -68,7 +68,7 @@ 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 @@ -119,7 +119,7 @@ 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 |