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...

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...

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.

Within the framework of the effective field theory, we examine the phase transitions of the spin-12 Ising film in a transverse field. We study the critical temperature of the film as a function of the exchange interactions, the transverse field and the film thickness. We find that, if the ratio...