Two-dimensional infinite repulsive systems: the Yang-Lee singularities are isolated branch points

Abstract

The singularities of the pressure as a function of the activity z are examined by a certain limiting procedure applicable to the solved hard-hexagon model (Baxter 1980) and the tempered hard-square model (Fisher 1963). For hard hexagons the only singularities found in the finite complex z plane are two isolated branch points on the real z axis. For the tempered hard squares, the only singularities found are three isolated branch points on the real z axis. By the same procedure applied to the Ising model, the singularities of the energy as a function of temperature are found to be isolated branch points in the complex temperature plane. Comparison with numerical results shows that the dense distribution of singularities of finite systems disappears in the finite system limit, save for a few isolated points.