A Monte Carlo study of the entropy, the pressure, and the critical behavior of the hard-square lattice gas

An approximate technique for estimating the entropyS with computer simulation methods, suggested recently by Meirovitch, is applied here to the Metropolis Monte Carlo (MC) simulation of the hard-square lattice gas in both the grand canonical and the canonical ensembles. The chemical potentialμ, calculated by Widom's method, andS enable one to obtain also the pressureP. The MC results are compared with results obtained with Padé approximants (PA) and are found to be very accurate; for example, at the critical activityzc the MC and the PA estimates forS deviate by 0.5%. Beyondzc this deviation decreases to 0.01% and comparable accuracy is detected forP. We argue that close tozc our results forS, μ, andP are more accurate than the PA estimates. Independent of the entropy study, we also calculate the critical exponents by applying Fisher's finite-size scaling theory to the results for the long-range order, the compressibility and the staggered compressibility, obtained for several lattices of different size at zc. The data are consistent with the critical exponents of the plane Ising latticeβ=1/8,ν=1,γ=7/4, andα=0. Our values forβ and ν agree with series expansion and renormalization group results, respectively,α=0 has been obtained also by matrix method studies; it differs, however, from the estimate of Baxteret al. α=0.09 ± 0.05. As far as we knowγ has not been calculated yet.

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