We study the m = 3 bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with probability p or 1 − p, respectively. Occupied sites with less than m occupied first-neighbours are then rendered unoccupied; this culling process is repeated until a stable configuration is reached. We evaluate the percolation critical probability, pc, and both scaling powers, yp and y h , and, contrarily to previous calculations, our results indicate that the model belongs to the same universality class as usual percolation (i.e., m = 0). The critical spanning probability, R(pc), is also numerically studied, for systems with linear sizes ranging from L = 32 up to L = 480: the value we found, R(pc) = 0.270 ± 0.005, is the same as for usual percolation with free boundary conditions.

The phase-diagram of the two-dimensional Blume-Capel model with a random crystal field is investigated within the framework of a real-space renormalization group approximation. Our results suggest that, for any amount of randomness, the model exhibits a line of Ising-like continuous transitions, as in the pure model, but no first-order transition. At zero temperature the transition is also continuous, but not in the same universality class as the Ising model. In this limit, the attractor (in the renormalization group sense) is the percolation fixed point of the site diluted spin-1/2 Ising model. The results we found are in qualitative agreement with general predictions made by Berker and Hui on the critical behaviour of random models. 75.10.Hk; 64.60.Ak; 64.60.Kw 30 kT J O D ∆ J 10 20 *

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We study the Blume-Emery-Griffiths model in a random crystal field in two and three dimensions, through a real-space renormalization-group approach and a mean-field approximation, respectively. According to the two-dimensional renormalization-group calculation, non-symmetry-breaking firstorder phase transitions are eliminated and symmetry-breaking discontinuous transitions are replaced by continuous ones, when disorder is introduced. On the other hand, the mean-field calculation predicts that first-order transitions are not eliminated by disorder, although some changes are introduced in the phase diagrams. We make some comments on the consequences of a degeneracy parameter, which may be relevant in martensitic transitions. 75.10.Hk; 64.60.Ak; 64.60.Kw 2 kT __ ∆ __ J z J

We study the thermodynamic and magnetic properties of an Ising bilayer ferrimagnet. The system is composed of two interacting non-equivalent planes in which the intralayer couplings are ferromagnetic while the interlayer interactions are antiferromagnetic. Moreover, one of the planes is randomly diluted. The study is carried out within a Monte Carlo approach employing the multiple histogram reweighting method and finite-size scaling tools. The occurrence of a compensation phenomenon is verified and the compensation temperature, as well as the critical temperature for the model, are obtained as functions of the Hamiltonian parameters. We present a detailed discussion of the regions of the parameter space where the compensation effect is present or absent. Our results are then compared to a mean-field-like approximation applied to the same model by Balcerzak and Sza{\l}owski (2014). Although the Monte Carlo and mean-field results agree qualitatively, our quantitative results are significantly different