Phase Transitions in Two-Dimensional Lattice Gases of Hard-Square Molecules

Abstract

The thermodynamic properties of lattice gases of hard‐square molecules on a two‐dimensional square lattice are investigated with special emphasis on the occurence of phase transitions. Three particular systems (called A, B, and C, respectively) are considered, corresponding to exclusion cores including (a) first neighboring sites, (b) first and second neighboring sites and (c) first, second, and third neighboring sites. Case A has already been extensively studied by several authors so that the original contribution of this paper essentially concerns Cases B and C. Three methods for computing the thermodynamic properties of these systems have been used: (a) the matrix method of Kramers and Wannier, (b) low‐ and high‐density series, and (c) an approximate method due to Rushbrooke and Scoins. The situation from the point of view of phase transitions seems to be as follows: Case A presents a second‐order continuous transition, Case B remains doubtful, although a first‐order transition seems to be ruled out, Case C presents a first‐order transition (of the fluid—solid type).