Bimodal-random field Blume-Capel model in the cluster variation method

The outcome of the bimodal random magnetic field acting up or down along the z-axis on the spins of spin-1 with equal probability is investigated by using the lowest approximation of the cluster-variation method in the Blume-Capel model. The equal probability, p = 21, causes the model to give phase transitions of the form either second-or first-order. The phase diagrams of the model are computed on the (D, kBT/J) and (h, kBT/J) planes by taking into account the thermal variations of the order-parameters. The obtained phase diagrams reveal different phase regions with ground state values of 1 and 1/2 in addition to tricritical and critical end points. Simple and double hysteresis loops are also observed in the model