Abstract |
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 μc=1.756 82(2) and the critical particle density as ρc=0.180(4). From the Binder ratio Q and susceptibility χ, the thermal and magnetic exponents are estimated as yt=1.51(1)≈3∕2 and yh=1.8748(8)≈15∕8, respectively, while the analyses of energylike quantities yield yt 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 yt=3∕2. 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 zint≈2.21 and the latter has zint≈1.60. |