Computer simulation of a grand canonical ensemble of rodlike molecules

A Monte Carlo method for simulating a grand canonical ensemble of semi-infinite lattice–gas systems is proposed. This method evaluates the largest eigenvalue of the Kramers–Wannier matrix by means of Markov chains. The method is applied to two-dimensional lattice–gas systems of dimers, trimers, and tetramers (having the length-to-width ratios of two, three, and four, respectively) as well as to molecules with equal side lengths. No first-order isotropic-to-aligned phase change is found for the rodlike systems. The tetramer system, however, indicates a probable higher-order phase change.