diff options
| -rw-r--r-- | when_annealed.bib | 73 | ||||
| -rw-r--r-- | when_annealed.tex | 4 |
2 files changed, 46 insertions, 31 deletions
diff --git a/when_annealed.bib b/when_annealed.bib index 6483eea..3247cbd 100644 --- a/when_annealed.bib +++ b/when_annealed.bib @@ -74,6 +74,19 @@ 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$p$-spin interaction spin glass model: the statics}, @@ -152,6 +165,19 @@ doi = {10.1103/physrevlett.124.078002} } +@unpublished{ElAlaoui_2020_Algorithmic, + author = {El Alaoui, Ahmed and Montanari, Andrea}, + title = {Algorithmic Thresholds in Mean Field Spin Glasses}, + year = {2020},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Spherical Mixed $p$-Spin Model}, @@ -179,15 +205,17 @@ doi = {10.1088/1742-5468/abe29f} } -@article{Folena_2023_On, +@unpublished{Folena_2023_On, author = {Folena, Giampaolo and Zamponi, Francesco}, title = {On weak ergodicity breaking in mean-field spin glasses}, year = {2023}, - month = {2}, + month = {Feb}, + archiveprefix = {arXiv}, 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, @@ -370,6 +398,19 @@ 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}, @@ -396,29 +437,3 @@ 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}, - 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}, - doi = {10.1002/cpa.21922} -} - 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 |