Inhomogeneous Glauber dynamics and the process of crystallization of a lattice gas

L. Šamaj, Jerome Percus

Research output: Contribution to journalArticle

Abstract

The model under consideration is a hard-core lattice gas in an external potential on a Bethe lattice with nonequilibrium time evolution governed by Glauber dynamics. A hierarchical decoupling of nonequilibrium correlations, motivated by and asymptotically providing the exact form of equilibrium multisite correlations in the inhomogeneous potential regime, is proposed. Application is made to the process of lattice gas crystallization, at high activity, from a spatially homogeneous fluid phase to an equilibrium crystal phase with unequal sublattice densities. The first few levels of the hierarchical decoupling give a consistent picture of two kinds of nonequilibrium instabilities-one leading to a sublattice density bifurcation, the other associated with an abrupt increase in densities and correlations in time.

Original languageEnglish (US)
Pages (from-to)495-512
Number of pages18
JournalJournal of Statistical Physics
Volume78
Issue number1-2
DOIs
StatePublished - Jan 1995

Fingerprint

Glauber Dynamics
Lattice Gas
Crystallization
Non-equilibrium
crystallization
Decoupling
decoupling
sublattices
gases
Bethe Lattice
Unequal
Crystal
Bifurcation
Fluid
fluids
crystals
Model

Keywords

  • density bifurcation
  • Glauber dynamics
  • inverse profile equation
  • Lattice gas

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Inhomogeneous Glauber dynamics and the process of crystallization of a lattice gas. / Šamaj, L.; Percus, Jerome.

In: Journal of Statistical Physics, Vol. 78, No. 1-2, 01.1995, p. 495-512.

Research output: Contribution to journalArticle

Šamaj, L. ; Percus, Jerome. / Inhomogeneous Glauber dynamics and the process of crystallization of a lattice gas. In: Journal of Statistical Physics. 1995 ; Vol. 78, No. 1-2. pp. 495-512.
@article{8e4792e772854a2ea33c3668d9f93707,
title = "Inhomogeneous Glauber dynamics and the process of crystallization of a lattice gas",
abstract = "The model under consideration is a hard-core lattice gas in an external potential on a Bethe lattice with nonequilibrium time evolution governed by Glauber dynamics. A hierarchical decoupling of nonequilibrium correlations, motivated by and asymptotically providing the exact form of equilibrium multisite correlations in the inhomogeneous potential regime, is proposed. Application is made to the process of lattice gas crystallization, at high activity, from a spatially homogeneous fluid phase to an equilibrium crystal phase with unequal sublattice densities. The first few levels of the hierarchical decoupling give a consistent picture of two kinds of nonequilibrium instabilities-one leading to a sublattice density bifurcation, the other associated with an abrupt increase in densities and correlations in time.",
keywords = "density bifurcation, Glauber dynamics, inverse profile equation, Lattice gas",
author = "L. Šamaj and Jerome Percus",
year = "1995",
month = "1",
doi = "10.1007/BF02183361",
language = "English (US)",
volume = "78",
pages = "495--512",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "1-2",

}

TY - JOUR

T1 - Inhomogeneous Glauber dynamics and the process of crystallization of a lattice gas

AU - Šamaj, L.

AU - Percus, Jerome

PY - 1995/1

Y1 - 1995/1

N2 - The model under consideration is a hard-core lattice gas in an external potential on a Bethe lattice with nonequilibrium time evolution governed by Glauber dynamics. A hierarchical decoupling of nonequilibrium correlations, motivated by and asymptotically providing the exact form of equilibrium multisite correlations in the inhomogeneous potential regime, is proposed. Application is made to the process of lattice gas crystallization, at high activity, from a spatially homogeneous fluid phase to an equilibrium crystal phase with unequal sublattice densities. The first few levels of the hierarchical decoupling give a consistent picture of two kinds of nonequilibrium instabilities-one leading to a sublattice density bifurcation, the other associated with an abrupt increase in densities and correlations in time.

AB - The model under consideration is a hard-core lattice gas in an external potential on a Bethe lattice with nonequilibrium time evolution governed by Glauber dynamics. A hierarchical decoupling of nonequilibrium correlations, motivated by and asymptotically providing the exact form of equilibrium multisite correlations in the inhomogeneous potential regime, is proposed. Application is made to the process of lattice gas crystallization, at high activity, from a spatially homogeneous fluid phase to an equilibrium crystal phase with unequal sublattice densities. The first few levels of the hierarchical decoupling give a consistent picture of two kinds of nonequilibrium instabilities-one leading to a sublattice density bifurcation, the other associated with an abrupt increase in densities and correlations in time.

KW - density bifurcation

KW - Glauber dynamics

KW - inverse profile equation

KW - Lattice gas

UR - http://www.scopus.com/inward/record.url?scp=34249759397&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34249759397&partnerID=8YFLogxK

U2 - 10.1007/BF02183361

DO - 10.1007/BF02183361

M3 - Article

AN - SCOPUS:34249759397

VL - 78

SP - 495

EP - 512

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -