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...

We consider the q-state Potts model on the triangular lattice with two- and three-site interactions in alternate triangular faces, and determine zeroes of the partition function numerically in the case of pure three-site interactions. On the basis of a rigorous reciprocal symmetry and results on...

In 1968 we published the solution of the ground state energy and wave function of the one-dimensional Hubbard model, and we also showed that there is no Mott transition in this model. Details of the analysis have never been published, however. As the Hubbard model has become increasingly...

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...

Symmetry and integrability relations for the three-state chiral Potts model on two-dimensional lattices are reviewed. Our detailed and systematic analysis leads to new integrability varieties for specific chiral Potts models including new integrable points for the standard antiferromagnetic...

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,...