The random-field Ising model with asymmetric bimodal probability distribution

作者：Hadjiagapiou I A^*

来源：Physica A: Statistical Mechanics and Its Applications , 2010, 389(19): 3945-3955.

DOI：10.1016/j.physa.2010.05.033

• Ising model
• Mean-field approximation
• Bimodal random field
• Landau theory
• Phase-diagram
• Tricritical point
• Phase transitions

The Ising model, in the presence of a random field, is investigated within the mean-field approximation based on Landau expansion. The random field is drawn from the bimodal probability distribution P(h) = p delta(h - h(0)) + (1 - p)delta(h + h(0)), where the probability p assumes any value within the interval [0, 1], asymmetric distribution. The prevailing transitions are of second-order but, for some values of p and h(0), first-order phase transitions take place for smaller temperatures and higher h(0), thus confirming the existence of a tricritical point. Also, the possible reentrant phenomena in the phase diagram (T-h(0) plane) occur for appropriate values of p and h(0). Using the variational principle, we determine the equilibrium equation for magnetization and solve it for both transitions and at the tricritical point in order to determine the magnetization profile with respect to h(0).

• 出版日期2010-10-1