The random-field Ising model with asymmetric bimodal probability distribution

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)=pδ(h−h0)+(1−p)δ(h+h0)P(h)=pδ(h−h0)+(1−p)δ(h+h0), where the probability pp assumes any value within the interval [0,1][0,1], asymmetric distribution. The prevailing transitions are of second-order but, for some values of pp and h0h0, first-order phase transitions take place for smaller temperatures and higher h0h0, thus confirming the existence of a tricritical point. Also, the possible reentrant phenomena in the phase diagram (T−h0T−h0 plane) occur for appropriate values of pp and h0h0. 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 h0h0.