We report exact results on the enumeration of close-packed dimers on a finite kagome lattice with general asymmetric dimer weights under periodic and cylindrical boundary conditions. For symmetric dimer weights, the resulting dimer generating functions reduce to very simple expressions, and we...

Seven coefficients in the high temperature series expansions for the zero-field susceptibility and the specific heat are derived for the planar classical Heisenberg model with biquadratic interactions. The critical temperatures and the susceptibility exponents are determined for cubic lattices.

We consider a model for ternary polymer mixtures with bi- and tri-functional monomers and solvent molecules embedded on a honeycomb lattice. We first show that the grand partition function of the model polymer mixture is equivalent to the partition function of an eight-vertex model on the same...

On the basis of the linked-graph expansion theorem established by one of us, it is shown that the modified F model in a small electric field is related to a two-dimensional nearest-neighbor Ising model in an external magnetic field. Applying this relation to the critical isotherm we get δ = 7,...

A ternary solution is considered in which molecules of types AA, BB, and AB occupy the bonds of a honeycomb lattice or a three-coordinate Bethe lattice. The three molecular ends near a common lattice site interact with arbitrary three-body interactions εAAA, εAAB, εABB and εBBB. The model is...

We consider a statistical mechanical model describing flux lines in type II superconductors by embedding the flux lines on a lattice wound on torus. The lines are nonintersecting and each loop of lines is associated with a fugacity z = −1. It is shown that the exact solution of this model...

The problem of close-packed dimers on the honeycomb lattice was solved by Kasteleyn in 1963. Here we extend the solution to include interactions between neighboring dimers in two spatial lattice directions. The solution is obtained by using the method of Bethe ansatz and by converting the dimer...

A general q-state nonintersecting string model for q≧2 is studied, and solved, using a graphical approach. This model, of which special cases were first introduced by Strogonov and Schultz, has recently drawn further attention because of its relation to Potts models. In its simplest version, a...

We consider the Ising model on an M×N rectangular lattice with an asymmetric self-dual boundary condition, and derive a closed-form expression for its partition function. We show that zeroes of the partition function are given by the roots of a polynomial equation of degree 2M−1, which trace...

The phase transition of the three-state chiral Potts model is investigated by Monte Carlo simulations performed on two types of isotropic triangular lattices of various linear sizes up to 128. These two types of model are shown to have different phase diagrams. In addition, the critical...