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 ${\mu }_c=1.75682\left(2\right)$ and the critical particle density as ${\rho }_c=0.180\left(4\right)$. From the Binder ratio $Q$ and susceptibility $\chi$, the thermal and magnetic exponents are estimated as $y_t=1.51\left(1\right)\approx 3∕2$ and $y_h=1.8748\left(8\right)\approx 15∕8$, 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 $y_t=3∕2$. 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 $z_{\mathrm{int}}\approx 2.21$ and the latter has $z_{\mathrm{int}}\approx 1.60$.

• Received 23 March 2008

DOI:https://doi.org/10.1103/PhysRevE.78.031103