Thermodynamical properties of the random field mixed spin transverse Ising model

The three-dimensional mixed spin transverse Ising system consisting of spin-((1)/(2)) and spin-1 with random longitudinal fields is investigated by the use of the finite cluster approximation. The random fields are assumed to be uncorrelated variables and obey the bimodal and trimodal distributions. In this approach, we derive the state equations using appropriate distributions accounting exactly for the single-site kinematic relations. In addition to the phase diagrams and magnetizations, which show qualitatively interesting features, we find a number of characteristic behaviours of the internal energy at low temperatures. The specific heat and zero-field magnetic susceptibility are also calculated and examined for both kinds of probability distributions