Monte Carlo study of the triangular lattice gas with first- and second-neighbor exclusions

We formulate a Swendsen-Wang-like version of the geometric cluster algorithm. As an application, we study the hard-core lattice gas on the triangular lattice with the first- and second-neighbor exclusions. The data were first analyzed by finite-size scaling without including logarithmic corrections. We determine the critical chemical potential as mu_{c}=1.75682(2) and the critical particle density as rho_{c}=0.180(4) . From the Binder ratio Q and susceptibility chi , the thermal and magnetic exponents are estimated as y_{t}=1.51(1) approximately 32 and y_{h}=1.8748(8) approximately 158 , respectively, while the analyses of energylike quantities yield y_{t} ranging from 1.440(5) to 1.470(5). Nevertheless, the data for energylike quantities are also well described by theoretically predicted scaling formulas with logarithmic corrections and with exponent y_{t}=32 . These results are very similar to the earlier study for the four-state Potts model on the square lattice [J. Stat. Phys. 88, 567 (1997)], and strongly support the general belief that the model is in the four-state Potts universality class. The dynamic scaling behavior of the Metropolis simulation and the combined method of the Metropolis and the geometric cluster algorithm is also studied; the former has a dynamic exponent z_{int} approximately 2.21 and the latter has z_{int} approximately 1.60 .