First-order phase transitions in hard-core lattice gases: I. Methods involving transfer matrices

Abstract

This is the first of two papers concerned with first-order phase transitions in two-dimensional hard-core lattice gases. We outline methods of utilising information from transfer-matrix studies of semi-infinite lattices to predict the location and nature of any phase transition in a lattice of infinite width. The methods are tested on three examples: the superexchange model (for which Fisher has calculated an exact isotherm), a square-lattice gas with an attractive potential extending to nearest-neighbour sites (mathematically equivalent to the spin- 1 2 Ising model whose behaviour in the transition region is known), and the square-lattice gas with nearest-neighbour exclusion (which has been studied independently by several different authors who agree on the transition parameters). The results of these tests are used to assess the numerical methods.