The problem of a two-dimensional lattice gas with nearest neighbor infinite repulsion is considered by obtaining exact solutions for a sequence of semi-infinite spaces. The exact solutions are obtained for M x spaces with 2 < M < 14 in even steps, and although there are no phase transitions in these spaces, a criterion for the point of "closest approach" to a phase transition is established. The values of the ther-modynamic variables evaluated at this point for each M are extrapolated to obtain the properties of the two-dimensionally infinite space. The data indicate a third-order phase transi¬tion occurring with probably infinite compressibility at an activity z = 3.799, a density Q/Q = 0.7356, and a pressure given by P/kbT = 0.7914. The density is obtained by a rigor¬ous differentiation of the secular determinant that determines the value of the pressure for a given z, thus securing the accuracy of the calculations and enabling the extrapolated values of the thermodynamic variables to be estimated with good precision.
展开▼
