Application of the Monte Carlo Method to the Lattice-Gas Model. I. Two-Dimensional Triangular Lattice

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Abstract
The Monte Carlo numerical method for obtaining statistical mechanical averages in the petite canonical ensemble has been applied to the two‐dimensional triangular lattice‐gas model. The Monte Carlo procedure described by Rosenbluth et al. and by Wood and Parker has been extended slightly to include the calculation of the partition function. The results are compared with the exact solutions for the two‐dimensional lattice and the agreement is well within the fluctuation displayed by the numerical method. The calculations are found to be relatively insensitive to a change in the pseudo‐random number sequence and to display no exceptional behavior in the region of the first‐order phase transition for small lattices.