Anisotropic four-state clock model in the presence of random fields.

A four-state clock ferromagnetic model is studied in the presence of different configurations of anisotropies and random fields. The model is considered in the limit of infinite-range interactions, for which the mean-field approach becomes exact. Both representations of Cartesian spin components and two Ising variables are used, in terms of which the physical properties and phase diagrams are discussed. The random fields follow bimodal probability distributions and the richest criticality is found when the fields, applied in the two Ising systems, are not correlated. The phase diagrams present new interesting topologies, with a wide variety of critical points, which are expected to be useful in describing different complex phenomena.

Phase diagrams of a spin-1 Ising system with competing short- and long-range interactions.

We have studied the phase diagrams of the one-dimensional spin-1 Blume-Capel model with anisotropy constant D, in which equivalent-neighbor ferromagnetic interactions of strength -J are superimposed on nearest-neighbor antiferromagnetic interactions of strength K. A rich critical behavior is found due to the competing interactions. At zero temperature two ordered phases exist in the D/J-K/J plane, namely the ferromagnetic (F) and the antiferromagnetic one (AF). For lower values of D/J(D/J<0.25) these two ordered phases are separated by the point K_{c}=0.25J. For 0.250.5, only phases AF and F exist and are separated by a line given by D/J=K/J. At finite temperatures, we found that the ferromagnetic region of the phase diagram in the k_{B}T/J-D/J plane is enriched by another ferromagnetic phase F^{^{'}} above a first-order line for 0.195

Multicritical behavior of two coupled Ising models in the presence of a random field.

A system defined by two coupled Ising models, with a bimodal random field acting in one of them, is investigated. The interactions among variables of each Ising system are infinite ranged, a limit where mean field becomes exact. This model is studied at zero temperature, as well as for finite temperatures, representing physical situations which are appropriate for describing real systems, such as plastic crystals. A very rich critical behavior is found, depending directly on the particular choices of the temperature, couplings, and random-field strengths. Phase diagrams exhibiting ordered, partially ordered, and disordered phases are analyzed, showing the sequence of transitions through all these phases, similarly to what occurs in plastic crystals. Due to the wide variety of critical phenomena presented by the model, its usefulness for describing critical behavior in other substances is also expected.