The Ising Mean-Field Model with Three-Spin Interaction and Magnetic Field

Carla Buzano

Godwin Osabutey

The equilibrium and phase properties of the Ising model with three-spin interaction and an external field are studied within the framework of mean-field approximation. The thermodynamic properties of the model reveals two coexistence curves, signifying two distinct second-order phase transitions, dependent on the domain of the interaction parameter. The critical exponents of the magnetic order parameter are calculated in all directions of the phase space and show their agreement with the mean-field universality class.

Gesualdo Delfino A, Giuseppe Mussardo

N. Hachem, M Alehyane, Amer Lafhal +4 more

Abstract The ferrimagnetic mixed spin-1/2 and spin-5/2 Ising model with a crystal field interaction in the absence and presence of a longitudinal magnetic field on a three-dimensional cubic lattice is studied within the framework both of the mean-field approximation (MFA) and Monte Carlo simulation (MCS). Using the MFA, we have shown the phase diagram of the model for zero magnetic field in the (anisotropy, temperature) plane in which the system exhibits first- and second-order phase transitions and critical end-points. Also, we have used the standard MCS to confirm the previous results; we have presented the temperature dependence of the sublattice and total magnetizations for different values of anisotropy in order to determine the phase diagram of the model in the absence of a longitudinal magnetic field. In addition, the influence of this last field on the magnetic properties of the model is investigated and discussed.

S. V. Semkin, Victor Smagin

Averaging over interaction fields and spin correlations in the Ising modelIn the theory of phase transitions in magnetic systems, there are a small number of exact results.One of them is the well-known Onsager solution for the Ising model on a square lattice.The problem of phase transitions in magnets is a special case of the problem of many bodies.There are many approaches and methods in this area, including the method of averaging over exchange fields.The application of the distribution function over interaction fields to the study of the properties of a system of many interacting particles has been used for a long time.In previous works of the authors, the method of averaging over exchange fields was applied to the analysis of the magnetic properties of pure and diluted magnets.In this paper, we formulate and prove the relations on which the method of averaging over exchange fields can be based on clusters of several spins.It turns out that based only on the possibility of representing thermodynamic means as means of the distribution function of the fields, some nontrivial exact relations can be obtained.The paper considers the Ising model on simple lattices with coordination numbers of three and four.Exact expressions are found that connect the average products of three spins with spontaneous magnetization in the system.Inequalities are obtained that limit the limiting value of the Curie temperature and the maximum value of spontaneous magnetization at a given temperature.