First-order phase transitions in hard-core lattice gases: II. Models on the square and triangular lattices

Abstract

This is the second of two papers on phase transitions in hard-core lattice gases. In the previous paper we discussed a number of methods of studying phase transitions in lattice gases by using information obtained from transfer matrices; we now apply these methods to three particular models. Our results support the case for a first-order transition in the square-lattice gas with first-, second-, and third-neighbour exclusion, and in the triangular-lattice gas with first- and second-neighbour exclusion. We have analysed Orban's data for the square-lattice gas with exclusion out to fourth-nearest neighbours, and conclude (with Orban) that the transition is probably continuous.