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Monte Carlo simulations of two-dimensional hard core lattice gases Heitor C. Marques Fernandes,a
 

Summary: Monte Carlo simulations of two-dimensional hard core lattice gases
Heitor C. Marques Fernandes,a
Jeferson J. Arenzon,b
and Yan Levinc
Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 Porto
Alegre RS, Brazil
Received 12 December 2006; accepted 16 January 2007; published online 21 March 2007
Monte Carlo simulations are used to study lattice gases of particles with extended hard cores on a
two-dimensional square lattice. Exclusions of one and up to five nearest neighbors NN are
considered. These can be mapped onto hard squares of varying side length, in lattice units , tilted
by some angle with respect to the original lattice. In agreement with earlier studies, the 1NN
exclusion undergoes a continuous order-disorder transition in the Ising universality class.
Surprisingly, we find that the lattice gas with exclusions of up to second nearest neighbors 2NN
also undergoes a continuous phase transition in the Ising universality class, while the Landau­
Lifshitz theory predicts that this transition should be in the universality class of the XY model with
cubic anisotropy. The lattice gas of 3NN exclusions is found to undergo a discontinuous
order-disorder transition, in agreement with the earlier transfer matrix calculations and the Landau­
Lifshitz theory. On the other hand, the gas of 4NN exclusions once again exhibits a continuous
phase transition in the Ising universality class--contradicting the predictions of the Landau­Lifshitz
theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase

  

Source: Arenzon, Jeferson J. - Instituto de Física, Universidade Federal do Rio Grande do Sul
Levin, Yan - Instituto de Física, Universidade Federal do Rio Grande do Sul

 

Collections: Physics