 
Summary: Monte Carlo simulations of twodimensional 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, 91501970 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
twodimensional 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 orderdisorder 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
orderdisorder 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 classcontradicting the predictions of the LandauLifshitz
theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase
