The random field Ising model in an asymmetric and anisotropic linearly field-dependent bimodal probability distribution

Abstract

The critical properties of the random-field Ising model are investigated by means of numerical analysis; the random field is drawn from the asymmetric and anisotropic linearly field-dependent bimodal probability distribution P(hi)=phiδ(hi−h0)+qhiδ(hi+λh0)=11+λ(λ+1h0)hiδ(hi−h0)+11+λ(1−1h0)hiδ(hi+λh0). The partial probabilities p,q are, in general, unequal (asymmetric distribution) such that p+q=1, hi is the random field with absolute value h0 and λ is a positive competition parameter making the two components of the distribution competitive, anisotropic distribution; the presence of the multiplicative factor hi is to enhance the influence of the magnetic fields. By obtaining data for several temperatures T, h0 and λ, the system possesses either only second order phase transitions or first and second order phase transitions joined smoothly at a tricritical point. Using the variational principle the equilibrium equation for the magnetization results and solve it for both transitions at any T and at the tricritical point, thus determining the phase diagram; the stability conditions for each phase transition and at the tricritical point are also examined.