S. R. Salinas

On the mean-field Ising model in a random external field

We use a method developed by van Hemmen to obtain the free energy of the mean-field Ising model in a random external magnetic field. Some results of previous mean-field calculations are confirmed and generalized. The tricritical point in the global phase diagram is discussed in detail. We also consider different probability distributions of the random fields and provide some proofs regarding the conditions for the existence of a tricritical point.

Metamagnets in uniform and random fields

We study a two-sublattice Ising metamagnet with nearest- and next-nearest-neighbor interactions, in both uniform and random fields. Using a mean-field approximation, we show that the qualitative features of the phase diagrams are significantly dependent on the distribution of the random fields. In particular, for a Gaussian distribution of random fields, the behavior of the model is qualitatively similar to a dilute Ising metamagnet in a uniform field.

Phase diagram of a random-anisotropy mixed-spin Ising model

We investigate the phase diagram of a mixed spin-1/2--spin-1 Ising system in the presence of quenched disordered anisotropy. We carry out a mean-field and a standard self-consistent Bethe--Peierls calculation. Depending on the amount of disorder, there appear novel transition lines and multicritical points. Also, we report some connections with a percolation problem and an exact result in one dimension.

Dimer pair correlations on the brick lattice

Using exact methods, pair-correlation functions are studied in the dimer model defined on a brick lattice. At long distances these functions exhibit strongly anisotropic algebraic decay and, near criticality, the length scales diverge differently in the two principal directions. The critical exponents are νx=1/2 and νy=1. These results are in agreement with deductions drawn from recent exact finite-size scaling calculations. We also interpret our results in the light of domain wall theories of commensurate-incommensurate transitions, and in particular we study the relation of the present model to the discrete version of the Pokrovsky-Talapov model introduced by Villain.

FOURTH-ORDER CUMULANTS TO CHARACTERIZE THE PHASE TRANSITIONS OF A SPIN-1 ISING MODEL

Fourth-order cumulants of physical quantities have been used to characterize the nature of a phase transition. In this paper we report some Monte Carlo simulations to illustrate the behavior of fourth-order cumulants of magnetization and energy across second and first-order transitions in the phase diagram of a well know spin-1 Ising model. Simple ideas from the theory of thermodynamic fluctuations are used to account for the behavior of these cumulants.

Mean-field phase diagram of the spin-1 Ising ferromagnet in a Gaussian random crystal field

The authors consider the mean-field version of a spin-1 Ising ferromagnet in a random crystal field described by a Gaussian probability distribution. Depending on the width of the Gaussian, they obtain a rich phase diagram, with critical and coexistence lines and some multicritical points. At low temperatures, their numerical results are supported by some analytic asymptotic expansions. They also calculate the ground state for a suitable two-valued delta-function distribution to compare with the results for the Gaussian case.

Statistical models of mixtures with a biaxial nematic phase

We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rodlike and disklike molecules. A quenched distribution of shapes leads to a phase diagram with two uniaxial and a biaxial nematic structure. A thermalized distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.

First-order transition in a spin-glass model

We consider a generalization of the infinite-range Sherrington-Kirkpatrick spin-glass model with arbitrary spin S and the inclusion of crystal-field effects. For integer S, replica-symmetric calculations have shown the presence of both continuous and discontinuous transitions and a tricritical point. For S=1, we report a detailed numerical analysis of the replica-symmetric solutions. We locate the first-order boundary and clarify some inconsistencies of the previous analyses. Some analytic asymptotic expansions are used to support the numerical findings.

Disorder and Competition in Soluble Lattice Models

Dilute systems lattice models with competing interactions spin glasses quantum lattice systems with competing interactions a brief introduction to dynamical system the theorems of Aubry Bethe Ansatz and conformal invariance unicity of phases, unicity in a sector, and spontaneous symmetry breaking.

The Blume-Emery-Griffiths model on a Bethe lattice: bicritical line and re-entrant behaviour

The authors analyse the global phase diagram of the Blume-Emery-Griffiths model on a Bethe lattice. As a function of coordination, they describe the main features of a staggered quadrupolar phase, and discuss the re-entrant character of some multicritical lines and phase boundaries. In the limit of infinite coordination, they regain the results of a two-sublattice mean-field calculation.