Monte Carlo simulations of 2d hard core lattice gases

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dc.creatorFernandes, Heitor C. Marques
dc.creatorArenzon, Jeferson J.
dc.creatorLevin, Yan
dc.date2006-12-14
dc.date.accessioned2026-07-07T07:52:44Z
dc.date.available2026-07-07T07:52:44Z
dc.descriptionMonte 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, $λ$ (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 Landau-Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase transition.
dc.description13 pages, lots of figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0612372
dc.identifierhttp://arxiv.org/abs/cond-mat/0612372
dc.identifierJ. Chem. Phys. 126, 114508 (2007) (11 pages)
dc.identifierdoi:10.1063/1.2539141
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125990
dc.subjectStatistical Mechanics
dc.subjectSoft Condensed Matter
dc.titleMonte Carlo simulations of 2d hard core lattice gases
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