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authorJaron Kent-Dobias <jaron@kent-dobias.com>2023-08-23 15:55:52 +0200
committerJaron Kent-Dobias <jaron@kent-dobias.com>2023-08-23 23:34:47 +0200
commitb8a0e53bfaca590fb6f7aa4f14a4f69630c6ff9c (patch)
tree909a8fe3e6baefe61eebe79ac85fc39ce512e687
parent4a9455031004be737f10a1a1a786a3de79c623fa (diff)
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Fixed some references at the request of a reviewer.
-rw-r--r--when_annealed.bib77
-rw-r--r--when_annealed.tex4
2 files changed, 49 insertions, 32 deletions
diff --git a/when_annealed.bib b/when_annealed.bib
index 3c5da60..65b6d1d 100644
--- a/when_annealed.bib
+++ b/when_annealed.bib
@@ -80,6 +80,19 @@
doi = {10.1103/physrevb.57.11251}
}
+@article{Cavagna_1999_Quenched,
+ author = {Cavagna, Andrea and Garrahan, Juan P and Giardina, Irene},
+ title = {Quenched complexity of the mean-field {$p$}-spin spherical model with external magnetic field},
+ journal = {Journal of Physics A: Mathematical and General},
+ publisher = {IOP Publishing},
+ year = {1999},
+ month = {1},
+ number = {5},
+ volume = {32},
+ pages = {711--723},
+ doi = {10.1088/0305-4470/32/5/004}
+}
+
@article{Crisanti_1992_The,
author = {Crisanti, A. and Sommers, H.-J.},
title = {The spherical $p$-spin interaction spin glass model: the statics},
@@ -164,6 +177,19 @@
doi = {10.1103/physrevlett.124.078002}
}
+@unpublished{ElAlaoui_2020_Algorithmic,
+ author = {El Alaoui, Ahmed and Montanari, Andrea},
+ title = {Algorithmic Thresholds in Mean Field Spin Glasses},
+ year = {2020},
+ month = {Sept},
+ archiveprefix = {arXiv},
+ date = {2020-09-24T04:22:42Z},
+ eprint = {2009.11481v1},
+ eprintclass = {cond-mat.stat-mech},
+ eprinttype = {arxiv},
+ primaryclass = {cond-mat.stat-mech}
+}
+
@article{Folena_2020_Rethinking,
author = {Folena, Giampaolo and Franz, Silvio and Ricci-Tersenghi, Federico},
title = {Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed $p$-Spin Model},
@@ -193,16 +219,22 @@
doi = {10.1088/1742-5468/abe29f}
}
-@article{Folena_2023_On,
+@unpublished{Folena_2023_On,
author = {Folena, Giampaolo and Zamponi, Francesco},
title = {On weak ergodicity breaking in mean-field spin glasses},
year = {2023},
+<<<<<<< HEAD
month = {2},
url = {http://arxiv.org/abs/2303.00026v2},
+=======
+ month = {Feb},
+ archiveprefix = {arXiv},
+>>>>>>> cf86b26 (Fixed some references at the request of a reviewer.)
date = {2023-02-28T19:02:47Z},
eprint = {2303.00026v2},
eprintclass = {cond-mat.dis-nn},
- eprinttype = {arxiv}
+ eprinttype = {arxiv},
+ primaryclass = {cond-mat.stat-mech}
}
@article{Fyodorov_2004_Complexity,
@@ -399,6 +431,19 @@
doi = {10.1103/physreve.51.5228}
}
+@article{Subag_2020_Following,
+ author = {Subag, Eliran},
+ title = {Following the Ground States of Full-{RSB} Spherical Spin Glasses},
+ journal = {Communications on Pure and Applied Mathematics},
+ publisher = {Wiley},
+ year = {2020},
+ month = {6},
+ number = {5},
+ volume = {74},
+ pages = {1021--1044},
+ doi = {10.1002/cpa.21922}
+}
+
@article{Wainrib_2013_Topological,
author = {Wainrib, Gilles and Touboul, Jonathan},
title = {Topological and Dynamical Complexity of Random Neural Networks},
@@ -427,31 +472,3 @@
doi = {10.1103/physrevlett.130.237101}
}
-@unpublished{ElAlaoui_2020_Algorithmic,
- author = {El Alaoui, Ahmed and Montanari, Andrea},
- title = {Algorithmic Thresholds in Mean Field Spin Glasses},
- year = {2020},
- month = {9},
- url = {http://arxiv.org/abs/2009.11481v1},
- archiveprefix = {arXiv},
- date = {2020-09-24T04:22:42Z},
- eprint = {2009.11481v1},
- eprintclass = {cond-mat.stat-mech},
- eprinttype = {arxiv},
- primaryclass = {cond-mat.stat-mech}
-}
-
-@article{Subag_2020_Following,
- author = {Subag, Eliran},
- title = {Following the Ground States of Full-{RSB} Spherical Spin Glasses},
- journal = {Communications on Pure and Applied Mathematics},
- publisher = {Wiley},
- year = {2020},
- month = {6},
- number = {5},
- volume = {74},
- pages = {1021--1044},
- url = {https://doi.org/10.1002%2Fcpa.21922},
- doi = {10.1002/cpa.21922}
-}
-
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