Title page for ETD etd-042399-073733


Type of Document Master's Thesis
Author Shaw, Leah Belinda
Author's Email Address lshaw@vt.edu
URN etd-042399-073733
Title Monte Carlo and Series Expansion Studies of the Anisotropic Driven Ising Lattice Gas Phase Diagram
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Hagedorn, George A. Committee Chair
Schmittmann, Beate Committee Member
Zia, Royce K. P. Committee Member
Keywords
  • Monte Carlo simulation
  • driven lattice gas
  • high temperature expansion
Date of Defense 1999-04-21
Availability unrestricted
Abstract
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 a. Under saturation drive, the shift in the transition temperature between ordered and disordered states can be either positive or negative, depending on a. The possible existence at large a 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 a-dependence of the critical temperature.

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