The Statistics of the Ising Ferromagnet.

J. R. Faleiro Ferreira, N. P. Silva

Abstract Approximate critical temperatures of anisotropic ferromagnetic Ising models are calculated through a recently proposed extended variational method in statistical mechanics. Using a linear chain Ising Hamiltonian in an effective field as trial Hamiltonian, quite good results are obtained.

B G S Doman

Hiroshi Mamada, F. Takano

Akaninyene Daniel Antia, Cyril C. Umoren

There is hardly any branch of physics one can approach successfully without resorting to quantum statistical mechanics.It has been proven that the quantum mechanical description of a system gives accurate results.To use quantum statistical mechanics, the system are treated at their microscopic level.Most systems consist of many particles and in order o deal with such large numbers, one has to resort to statistical method related to the partition function of statistical mechanics.In this study, we haves used the partition function which is a statistical parameter to explore the thermodynamic properties such as Helmoltz free energy, Entropy, internal energy and heat capacity of a magnetic materials in a ferromagnetic system using the first and second dimensional Ising model.The results show that in one-dimensional model, phase transition does not occur at finite temperature but susceptibility of a system can be measured from the fluctuations in the magnetization in the second dimensional Ising model.

T. H. Berlin, Mark Kac

A mathematical model, the spherical model, of a ferromagnet is described. The model is a generalization of the Ising model; and one-, two-, and three-dimensional lattices of infinite extent can be extensively discussed. A three-dimensional lattice shows ferromagnetic behavior and provides a statistical model of the Weiss phenomenological theory. The limiting free energy appears in a form which contains two of the essential features of the exactly known Ising model results in one and two dimensions. This suggests the probable form of the limiting free energy for the three-dimensional Ising model. A simplified model, the Gaussian model, is briefly discussed because this model also contains some of the significant features of the Ising model. However, the Gaussian model, unlike the spherical model, is not defined for all temperatures.

Jonathan V. Selinger