Free Energy and Complexity of Spherical Bipartite Models

Antonio Auffinger; Wei Kuo Chen

doi:10.1007/s10955-014-1073-0

Free Energy and Complexity of Spherical Bipartite Models

Antonio Auffinger^*, Wei Kuo Chen

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We investigate both free energy and complexity of the spherical bipartite spin glass model. We first prove a variational formula in high temperature for the limiting free energy based on the well-known Crisanti–Sommers representation of the mixed p-spin spherical model. Next, we show that the mean number of local minima at low levels of energy is exponentially large in the size of the system and we derive a bound on the location of the ground state energy.

Original language	English (US)
Pages (from-to)	40-59
Number of pages	20
Journal	Journal of Statistical Physics
Volume	157
Issue number	1
DOIs	https://doi.org/10.1007/s10955-014-1073-0
State	Published - Oct 1 2014

Keywords

Bipartite models
Complexity
Free energy
Spin glasses

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1007/s10955-014-1073-0

Fingerprint Dive into the research topics of 'Free Energy and Complexity of Spherical Bipartite Models'. Together they form a unique fingerprint.

Cite this

@article{0fa11ddc481d45719b594b29c957d967,

title = "Free Energy and Complexity of Spherical Bipartite Models",

abstract = "We investigate both free energy and complexity of the spherical bipartite spin glass model. We first prove a variational formula in high temperature for the limiting free energy based on the well-known Crisanti–Sommers representation of the mixed p-spin spherical model. Next, we show that the mean number of local minima at low levels of energy is exponentially large in the size of the system and we derive a bound on the location of the ground state energy.",

keywords = "Bipartite models, Complexity, Free energy, Spin glasses",

author = "Antonio Auffinger and Chen, {Wei Kuo}",

year = "2014",

month = oct,

day = "1",

doi = "10.1007/s10955-014-1073-0",

language = "English (US)",

volume = "157",

pages = "40--59",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Free Energy and Complexity of Spherical Bipartite Models

AU - Auffinger, Antonio

AU - Chen, Wei Kuo

PY - 2014/10/1

Y1 - 2014/10/1

N2 - We investigate both free energy and complexity of the spherical bipartite spin glass model. We first prove a variational formula in high temperature for the limiting free energy based on the well-known Crisanti–Sommers representation of the mixed p-spin spherical model. Next, we show that the mean number of local minima at low levels of energy is exponentially large in the size of the system and we derive a bound on the location of the ground state energy.

AB - We investigate both free energy and complexity of the spherical bipartite spin glass model. We first prove a variational formula in high temperature for the limiting free energy based on the well-known Crisanti–Sommers representation of the mixed p-spin spherical model. Next, we show that the mean number of local minima at low levels of energy is exponentially large in the size of the system and we derive a bound on the location of the ground state energy.

KW - Bipartite models

KW - Complexity

KW - Free energy

KW - Spin glasses

UR - http://www.scopus.com/inward/record.url?scp=84956797347&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84956797347&partnerID=8YFLogxK

U2 - 10.1007/s10955-014-1073-0

DO - 10.1007/s10955-014-1073-0

M3 - Article

AN - SCOPUS:84956797347

VL - 157

SP - 40

EP - 59

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1

ER -