The quadrupole phase transition of a planar classical Heisenberg model with biquadratic interactions is investigated by the high-temperature series expansion method. From the quadrupole susceptibility series the critical temperatures and the critical exponents are determined for cubic lattices.

The cluster variation method is applied to study critical properties of the Potts-like ferromagnetic anisotropic exchange interaction model. Phase transition temperatures, order parameter discontinuities and latent heats of the model on the triangular and the fcc lattices are determined by the...

In this paper we continue our consideration of closed-packed dimers on the kagome lattice. Using the Pfaffian approach we evaluate the correlation between dimers on two lattice edges. It is found that the correlation is extremely short-ranged in the case of symmetric dimers weights. Explicit...

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...

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...

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...