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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 latticewith the first- and the second-neighbor exclusions. The data are analyzed byfinite-size scaling, but the possible existence of logarithmic corrections isnot considered due to the limited data. We determine the critical chemicalpotential as $\mu_c=1.75682 (2)$ and the critical particle density as$\rho_c=0.180(4)$. The thermal and magnetic exponents $y_t=1.51(1) \approx 3/2$and $y_h=1.8748 (8) \approx 15/8$, estimated from Binder ratio $Q$ andsusceptibility $\chi$, strongly support the general belief that the model is inthe 4-state Potts universality class. On the other hand, the analyses ofenergy-like quantities yield the thermal exponent $y_t$ ranging from $1.440(5)$to $1.470(5)$. These values differ significantly from the expected value 3/2,and thus imply the existence of logarithmic corrections.

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