Glauber dynamics for spin systems at high and critical temperatures

Eyal Lubetzky

doi:10.1142/9789814304634_0036

Glauber dynamics for spin systems at high and critical temperatures

Eyal Lubetzky

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

The spectral gap of the continuous-time heat-bath Glauber dynamics for the Ising model on the lattice is believed to exhibit the following behavior. For some critical-inverse temperature β_c, the mixing-time of the dynamics is logarithmic in the surface-area for β “ β_c, polynomial for β = β_c and exponential for β > β_c. Furthermore, for β “ β_c the mixing time is sharply concentrated and the dynamics exhibits the cutoff phenomenon, an abrupt convergence to equilibrium. We survey the recent progress in confirming this picture for various underlying geometries and spin system models.

Original language	English (US)
Title of host publication	XVIth International Congress on Mathematical Physics
Publisher	World Scientific Publishing Co.
Pages	464-469
Number of pages	6
ISBN (Electronic)	9789814304634
ISBN (Print)	981430462X, 9789814304627
DOIs	https://doi.org/10.1142/9789814304634_0036
State	Published - Jan 1 2010

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

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title = "Glauber dynamics for spin systems at high and critical temperatures",

abstract = "The spectral gap of the continuous-time heat-bath Glauber dynamics for the Ising model on the lattice is believed to exhibit the following behavior. For some critical-inverse temperature βc, the mixing-time of the dynamics is logarithmic in the surface-area for β “ βc, polynomial for β = βc and exponential for β > βc. Furthermore, for β “ βc the mixing time is sharply concentrated and the dynamics exhibits the cutoff phenomenon, an abrupt convergence to equilibrium. We survey the recent progress in confirming this picture for various underlying geometries and spin system models.",

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N2 - The spectral gap of the continuous-time heat-bath Glauber dynamics for the Ising model on the lattice is believed to exhibit the following behavior. For some critical-inverse temperature βc, the mixing-time of the dynamics is logarithmic in the surface-area for β “ βc, polynomial for β = βc and exponential for β > βc. Furthermore, for β “ βc the mixing time is sharply concentrated and the dynamics exhibits the cutoff phenomenon, an abrupt convergence to equilibrium. We survey the recent progress in confirming this picture for various underlying geometries and spin system models.

AB - The spectral gap of the continuous-time heat-bath Glauber dynamics for the Ising model on the lattice is believed to exhibit the following behavior. For some critical-inverse temperature βc, the mixing-time of the dynamics is logarithmic in the surface-area for β “ βc, polynomial for β = βc and exponential for β > βc. Furthermore, for β “ βc the mixing time is sharply concentrated and the dynamics exhibits the cutoff phenomenon, an abrupt convergence to equilibrium. We survey the recent progress in confirming this picture for various underlying geometries and spin system models.

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BT - XVIth International Congress on Mathematical Physics

PB - World Scientific Publishing Co.

ER -

Glauber dynamics for spin systems at high and critical temperatures

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