On the Dimer Problem and the Ising Problem in Finite 3-dimensional Lattices

ar X iv : h ep - l at / 9 30 70 18 v 1 2 7 Ju l 1 99 3 The Ising model on spherical lattices : dimer versus

We study, using dimer and Monte Carlo approaches, the critical properties and finite size effects of the Ising model on honeycomb lattices folded on the tetrahedron. We show that the main critical exponents are not affected by the presence of conical singularities. The finite size scaling of the position of the maxima of the specific heat does not match, however, with the scaling of the correla...

On the Dimer Problem and the Ising Problem inFinite 3 - dimensional

Monomer-dimer model in two-dimensional rectangular lattices with fixed dimer density.

The classical monomer-dimer model in two-dimensional lattices has been shown to belong to the "#P-complete" class, which indicates the problem is computationally "intractable." We use exact computational method to investigate the number of ways to arrange dimers on mxn two-dimensional rectangular lattice strips with fixed dimer density rho . For any dimer density 0<rho<1 , we find a logarithmic...

An Algorithm based on Predicting the Interface in Phase Change Materials

Phase change materials are substances that absorb and release thermal energy during the process of melting and freezing. This characteristic makes phase change material (PCM)  a favourite choice to integrate it in buildings. Stephan problem including melting and solidification in PMC materials is an practical problem in many engineering processes. The position of the moving boundary, its veloci...

Two-dimensional Axisymmetric Electromechanical Response of Piezoelectric, Functionally Graded and Layered Composite Cylinders

A mixed semi-analytical cum numerical approach is presented in this paper which accounts for the coupled mechanical and electrical response of piezoelectric, functionally graded (FG) and layered composite hollow circular cylinders of finite length. Under axisymmetric mechanical and electrical loadings, the three-dimensional problem (3D) gets reduced to a two-dimensional (2D) plane strain proble...