Large deviation approach to the generalized random energy model

T C Dorlas, W M B Dukes

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The generalized random energy model is a generalization of the random energy model introduced by Derrida to mimic the ultrametric structure of the Parisi solution of the Sherrington–Kirkpatrick model of a spin glass. It was solved exactly in two special cases by Derrida and Gardner. A complete solution for the thermodynamics in the general case was given by Capocaccia et al. Here we use large deviation theory to analyse the model in a very straightforward way. We also show that the variational expression for the free energy can be evaluated easily using the Cauchy–Schwarz inequality.
LanguageEnglish
Pages4385-4394
Number of pages10
JournalJournal of Physics A: Mathematical and Theoretical
Volume35
Issue number20
DOIs
Publication statusPublished - 10 May 2002

Fingerprint

Energy Model
Large Deviations
Large Deviation Theory
Cauchy-Schwarz inequality
deviation
Spin Glass
Free Energy
Thermodynamics
Spin glass
energy
Model
spin glass
Free energy
free energy
thermodynamics
Generalization

Keywords

  • condensed matter
  • statistical physics
  • nonlinear systems
  • spin-glass
  • thermodynamic functions

Cite this

Dorlas, T C ; Dukes, W M B. / Large deviation approach to the generalized random energy model. In: Journal of Physics A: Mathematical and Theoretical. 2002 ; Vol. 35, No. 20. pp. 4385-4394.
@article{498962ccb3834267ada1efc8b9939228,
title = "Large deviation approach to the generalized random energy model",
abstract = "The generalized random energy model is a generalization of the random energy model introduced by Derrida to mimic the ultrametric structure of the Parisi solution of the Sherrington–Kirkpatrick model of a spin glass. It was solved exactly in two special cases by Derrida and Gardner. A complete solution for the thermodynamics in the general case was given by Capocaccia et al. Here we use large deviation theory to analyse the model in a very straightforward way. We also show that the variational expression for the free energy can be evaluated easily using the Cauchy–Schwarz inequality.",
keywords = "condensed matter, statistical physics, nonlinear systems, spin-glass, thermodynamic functions",
author = "Dorlas, {T C} and Dukes, {W M B}",
year = "2002",
month = "5",
day = "10",
doi = "10.1088/0305-4470/35/20/301",
language = "English",
volume = "35",
pages = "4385--4394",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "0305-4470",
number = "20",

}

Large deviation approach to the generalized random energy model. / Dorlas, T C; Dukes, W M B.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 35, No. 20, 10.05.2002, p. 4385-4394.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Large deviation approach to the generalized random energy model

AU - Dorlas, T C

AU - Dukes, W M B

PY - 2002/5/10

Y1 - 2002/5/10

N2 - The generalized random energy model is a generalization of the random energy model introduced by Derrida to mimic the ultrametric structure of the Parisi solution of the Sherrington–Kirkpatrick model of a spin glass. It was solved exactly in two special cases by Derrida and Gardner. A complete solution for the thermodynamics in the general case was given by Capocaccia et al. Here we use large deviation theory to analyse the model in a very straightforward way. We also show that the variational expression for the free energy can be evaluated easily using the Cauchy–Schwarz inequality.

AB - The generalized random energy model is a generalization of the random energy model introduced by Derrida to mimic the ultrametric structure of the Parisi solution of the Sherrington–Kirkpatrick model of a spin glass. It was solved exactly in two special cases by Derrida and Gardner. A complete solution for the thermodynamics in the general case was given by Capocaccia et al. Here we use large deviation theory to analyse the model in a very straightforward way. We also show that the variational expression for the free energy can be evaluated easily using the Cauchy–Schwarz inequality.

KW - condensed matter

KW - statistical physics

KW - nonlinear systems

KW - spin-glass

KW - thermodynamic functions

UR - http://iopscience.iop.org/0305-4470

U2 - 10.1088/0305-4470/35/20/301

DO - 10.1088/0305-4470/35/20/301

M3 - Article

VL - 35

SP - 4385

EP - 4394

JO - Journal of Physics A: Mathematical and Theoretical

T2 - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 0305-4470

IS - 20

ER -