Effects of on-site disorder in the critical behavior of the Blume Capel model

The Blume-Capel model is a classical spin model in which vacancies are allowed. The model, even in the two-dimensional square lattice for ferromagnetic interactions, exhibits a rich phase diagram with a tri-critical point. In this study, we investigate the behavior of the Blume-Capel model in the two-dimensional square lattice in the presence of a random on-site disorder in the crystal field. We have developed an exact enumeration code and a Monte Carlo simulation with cluster updates to explore the phase diagram of the model as the degree of Gaussian disorder is varied. We compute the magnetization, specific heat, magnetic susceptibility, and Edwards-Anderson parameter to locate the phase boundaries under averages over the disorder. We present our results in understanding how the presence of disorder modifies the critical behavior of the model.