Uncovering the secrets of the 2D random-bond Blume–Capel model

The effects of bond randomness on the ground-state structure, phase diagram and critical behavior of the square lattice ferromagnetic Blume–Capel (BC) model are discussed. The calculation of ground states at strong disorder and large values of the crystal field is carried out by mapping the system onto a network and we search for a minimum cut by a maximum flow method. At finite temperatures the system is studied by an efficient two-stage Wang–Landau (WL) method for several values of the crystal field, including both the first- and second-order phase transition regimes of the pure model. We attempt to explain the enhancement of ferromagnetic order and we discuss the critical behavior of the random-bond model. Our results provide evidence for a strong violation of universality along the second-order phase transition line of the random-bond version.