The random field Ising model in a shifted bimodal probability distribution

The critical behavior of the Ising model in the presence of a random magnetic field is investigated for any temperature T. The random field is drawn from the proposed shifted bimodal probability distribution P(hi)=(12+12h0)hiδ(hi−h0)+(12−12h0)hiδ(hi+h0), hi is the random field variable with strength h0. By obtaining data for several transition temperatures T and random field strengths h0, we conclude that the system possesses first and second order phase transitions, joined smoothly at a tricritical point, with coordinates (TTCP,h0TCP,V0TCP)=(1.5775571,3.7348565,−4.7741775), where V0 is an auxiliary field. Using the variational principle, we determine the phase diagram and the equilibrium equation for magnetization (with zero and nonzero values), solve it for both transitions and at the tricritical point and examine the stability conditions of each phase transition.