summaryrefslogtreecommitdiff
path: root/frsb_kac-rice.tex
diff options
context:
space:
mode:
authorJaron Kent-Dobias <jaron@kent-dobias.com>2022-07-08 16:46:07 +0200
committerJaron Kent-Dobias <jaron@kent-dobias.com>2022-07-08 16:46:07 +0200
commite5ca8fbdc08097cb17fd97de44ce9c103e56a303 (patch)
treef25425a527370bbf1012380d1f02b434355f97bc /frsb_kac-rice.tex
parent237092a616219c3fab36e9bbb78f15c74d60f3a3 (diff)
downloadPRE_107_064111-e5ca8fbdc08097cb17fd97de44ce9c103e56a303.tar.gz
PRE_107_064111-e5ca8fbdc08097cb17fd97de44ce9c103e56a303.tar.bz2
PRE_107_064111-e5ca8fbdc08097cb17fd97de44ce9c103e56a303.zip
Some tweaks and new title proposal
Diffstat (limited to 'frsb_kac-rice.tex')
-rw-r--r--frsb_kac-rice.tex26
1 files changed, 17 insertions, 9 deletions
diff --git a/frsb_kac-rice.tex b/frsb_kac-rice.tex
index 23a41d4..6880717 100644
--- a/frsb_kac-rice.tex
+++ b/frsb_kac-rice.tex
@@ -15,7 +15,10 @@
\addbibresource{frsb_kac-rice.bib}
\begin{document}
-\title{Full solution for counting stationary points of mean-field complex energy landscapes}
+\title{Full solution for counting stationary points of mean-field complex energy landscapes\\
+ \textit{or (fun title)} \\
+ How to count in hierarchical landscapes: a `full' solution to mean-field complexity
+}
\author{Jaron Kent-Dobias \& Jorge Kurchan}
\maketitle
\begin{abstract}
@@ -25,14 +28,19 @@
\section{Introduction}
The computation of the number of metastable states of mean field spin glasses
-goes back to the beginning of the field. Over forty years ago,
-Bray and Moore \cite{Bray_1980_Metastable} attempted the first calculation for
- the Sherrington--Kirkpatrick model, in a paper remarkable for being one of the first applications of a replica symmetry breaking scheme. As became clear when the actual ground-state of the model was computed by Parisi \cite{Parisi_1979_Infinite} with a different scheme, the Bray--Moore result
- was not exact, and in fact the problem has been open ever since.
-To this date the program of computing the number of saddles of a mean-field
-glass has been only carried out for a small subset of models, including most notably the (pure) $p$-spin model ($p>2$) \cite{Rieger_1992_The, Crisanti_1995_Thouless-Anderson-Palmer}.
-In a parallel development, it
-has evolved into an active field in probability theory \cite{Auffinger_2012_Random, Auffinger_2013_Complexity, BenArous_2019_Geometry}
+goes back to the beginning of the field. Over forty years ago, Bray and Moore
+\cite{Bray_1980_Metastable} attempted the first calculation for the
+Sherrington--Kirkpatrick model, in a paper remarkable for being one of the
+first applications of a replica symmetry breaking scheme. As became clear when
+the actual ground-state of the model was computed by Parisi
+\cite{Parisi_1979_Infinite} with a different scheme, the Bray--Moore result was
+not exact, and in fact the problem has been open ever since. To this date the
+program of computing the number of saddles of a mean-field glass has been only
+carried out for a small subset of models, including most notably the (pure)
+$p$-spin model ($p>2$) \cite{Rieger_1992_The,
+Crisanti_1995_Thouless-Anderson-Palmer}. In a parallel development, it has
+evolved into an active field in probability theory \cite{Auffinger_2012_Random,
+Auffinger_2013_Complexity, BenArous_2019_Geometry}.
In this paper we present what we argue is the general replica ansatz for the
computation of the number of saddles of generic mean-field models, which we expect to include the Sherrington--Kirkpatrick model. It reproduces the Parisi result in the limit