We consider an explicit finite element approximation of a model for phase separation in a ternary mixture and describe some numerical experiments in two space dimensions.

The Pair Approximation method is applied to the antiferromagnetic Heisenberg–Ising spin- 1/2 bilayer with a simple cubic crystalline structure. The method allows for self-consistent calculations of thermodynamic quantities, based on the determination of Gibbs free-energy. In the paper the...

The Pair Approximation method is applied to studies of the bilayer and multilayer magnetic systems with simple cubic structure. The method allows to take into account quantum effects related to non-Ising couplings. The paper adopts the anisotropic Heisenberg model for spin S=1/2 and considers...

Using the Huang–Yang–Luttinger and Lee–Yang virial expansions of a dilute Bose gas as well as our theory of phase transition, we show that in the dilute limit, the critical temperature of Bose–Einstein condensation of a Bose gas is given by [Tc−Tc(0)]/Tc(0)=γn1/3a,...

This paper revisits the fundamental statistical properties of the crucial model in critical phenomena i.e., the Ising model, guided by our knowledge of the energy values of the Ising Hamiltonian and aided by numerical estimation techniques. We have obtained exact energies in 2D and 3D and nearly...

By using a decomposition of the transfer matrix of the q-state Potts model on a three-dimensional m×n×n simple cubic lattice its determinant is calculated exactly. By using the calculated determinants, a formula is conjectured that approximates the critical temperature for a d-dimensional...

The site-diluted Ising model has been investigated using an improved microcanonical algorithm from Creutz Cellular Automaton. For a microcanonical algorithm, the basic problem is to estimate the correct temperatures using average values of the kinetic energy in the simulations of site-diluted...

Spin correlation identities for the Blume–Capel model on Kagome lattice are derived and combined with rigorous correlation inequalities lead to upper bounds on the critical temperature. From the spin correlation identities the mean field approximation and the effective field approximation...

In the present paper we obtain rates of convergence for limit theorems via Stein’s Method of exchangeable pairs in the context of the Curie–Weiss–Potts model and we consider only the case of non-zero external field h∈Rq. Our interest is in the limit distribution of the empirical vector...

The phase transitions of a ferromagnet spin-1/2 Ising superlattice consisting of two different materials are examined using the effective field theory. The critical temperature of the system is studied as a function of the thickness of the constituents in a unit cell, exchange interactions in...