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The effects of bond randomness on the phase diagram and critical behavior ofthe square lattice ferromagnetic Blume-Capel model are discussed. The system isstudied in both the pure and disordered versions by the same efficienttwo-stage Wang-Landau method for many values of the crystal field, restrictedhere in the second-order phase transition regime of the pure model. For therandom-bond version several disorder strengths are considered. We present phasediagram points of both pure and random versions and for a particular disorderstrength we locate the emergence of the enhancement of ferromagnetic orderobserved in an earlier study in the ex-first-order regime. The criticalproperties of the pure model are contrasted and compared to those of the randommodel. Accepting, for the weak random version, the assumption of the doublelogarithmic scenario for the specific heat we attempt to estimate the range ofuniversality between the pure and random-bond models. The behavior of thestrong disorder regime is also discussed and a rather complex and yet not fullyunderstood behavior is observed. It is pointed out that this complexity isrelated to the ground-state structure of the random-bond version.

physical review. e, statistical, nonlinear and soft matter physics

Multicritical Points and Crossover Mediating the Strong Violation of  Universality: Wang-Landau Determinations in the Random-Bond $d=2$ Blume-Capel  model