Monte Carlo and Series Expansion Studies of the Anisotropic Driven Ising Lattice Gas Phase Diagram

While the statistical mechanics of systems in thermal equilibrium is a well established discipline, nonequilibrium systems are fundamentally much less well understood, even though most natural phenomena fall into the latter category. In particular, there is as yet no nonequilibrium analog for the systematic formalism of Gibbs ensembles. Rather than deal with the difficult problem of general nonequilibrium systems, this study is restricted to the steady states of a simple model whose equilibrium properties are well known. The Ising lattice gas displays a number of surprising phenomena when driven into nonequilibrium steady states. This study extends previous work to a more general model with anisotropic interparticle interactions. Using Monte Carlo simulations, we obtain the phase diagram for the model, controlled by the driving field, temperature, and anisotropy parameter α. Under saturation drive, the shift in the transition temperature between ordered and disordered states can be either positive or negative, depending on α ≡ √(𝐽_∥/𝐽_⟂). The possible existence at large α of an additional phase ordered in only one direction is discussed. For finite drives, both first and second order transitions are observed. A novel technique for locating the first order transition line is presented. Some aspects of the phase diagram can be predicted by investigating the two-point correlation function to first order in a high temperature series expansion. However, the series expansion fails to predict even qualitatively the α-dependence of the critical temperature.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1999

Author dc:creator

• Shaw, Leah Belinda

Chair dc:contributor.committeechair

• Hagedorn, George A.

Committee members dc:contributor.committeemember

• Zia, Royce K. P.
• Schmittmann, Beate

• Monte Carlo simulation
• driven lattice gas
• high temperature expansion

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-042399-073733

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/31851