A new calculation method for partition functions in some lattice models

А. А. Зайцев

R. J. Baxter

Michael J. Velgakis

A new method is proposed for the calculation of the exact partition function for Ising-like systems, based on finite-lattice arguments. In a way, the method is originated with the finite scaling theories presented by Bhanot [J. Stat. Phys. 60, 55 (1990)] and earlier by Binder [Physica 62, 508 (1972)]. The method is tested on a 2D Ising model with nearest- and next-nearest-neighbors interactions. An asset of the method is the low computer power demand.

Nelson A. Alves, J. R. Drugowich de Felício, Ulrich H. E. Hansmann

A general numerical method is presented to locate the partition function zeros in the complex β plane for large lattice sizes. We apply this method to the 2D Ising model and results are reported for square lattice sizes up to L = 64. We also propose an alternative method to evaluate corrections to scaling which relies only on the leading zeros. This method is illustrated with our data.

R. J. Baxter

R. B. Potts, John Ward

A combinational method is used to calculate (a) the partition function of a finite rectangular Ising lattice and (b) the correlation functions of an infinite lattice.