Francisco A. da Costa

m-Vector spin glasses in the presence of uniaxial anisotropies

Abstract The effects of the two lowest-order uniaxial anisotropy fields on the phase diagrams of the classical m -vector spin glass are analyzed. The model is defined in terms of infinite–range interactions and the replica approach is used to study the system. The replica-symmetric phase diagrams present qualitative modifications with respect to those with no uniaxial anisotropies; new features, in particular, reentrance effects arise. In some cases, the reentrant critical frontiers are totally inside the region of instability of the replica-symmetric solution and may disappear within more general parametrizations, whereas in other cases, they coincide with the limit of stability of such a solution and should persist under replica-symmetry breaking.

Spin-glass model with uniform biquadratic interactions

We study a spin-1 infinite-ranged Ising spin-glass model with uniform biquadratic exchange interactions. The phase diagram of the model is obtained in the framework of the replica-symmetric solution. For the case of attractive biquadratic interactions the usual spin-glass phase is stabilized at low temperatures, but for the repulsive case, the antiquadrupolar and antiquadrupolar-glass phases with two-sublattice structure are also possible. We investigate the stability of the replica-symmetric solution and show that the paramagnetic and antiquadrupolar phases are stable, whereas the spin-glass and antiquadrupolar-glass phases are unstable. Parisis replica-symmetry-breaking procedure is implemented in the neighbourhood of the spin-glass - paramagnetic critical frontier.

Random-energy model in random fields

The random-energy model is studied in the presence of random fields. The problem is solved exactly both in the microcanonical ensemble, without recourse to the replica method, and in the canonical ensemble using the replica formalism. The phase diagrams for bimodal and Gaussian random fields are investigated in detail. In contrast to the Gaussian case, the bimodal random field may lead to a tricritical point and a first-order transition. An interesting feature of the phase diagram is the possibility of a first-order transition from paramagnetic to mixed phase.

The spin-1 Ising spin glass: a renormalization-group approach

The nearest-neighbour-interaction spin-1 Ising spin glass, in the presence of a random crystal field, is considered on diamond hierarchical lattices of fractal dimensions d = 2, 3 and 4. The coupling constants and crystal fields follow Gaussian probability distributions, which are taken as independent, at the beginning of the iteration process. By monitoring simultaneously the evolution of two probability distributions, associated respectively with the renormalized coupling constants and crystal fields, the phase diagrams of the model are obtained. A spin-glass phase, at finite temperatures, is found for hierarchical lattices with d = 3 and 4, but not for d = 2. Two distinct attractors characterized by zero effective coupling constants are detected. Following the usual procedure, i.e. associating an equilibrium phase with each basin of attraction, one obtains two phases with absence of magnetic order, namely, a zero-spin phase (where the spins prefer the 0 state) and a ±1-spin phase (where the spins prefer ±1 states at random).

Stability of a two-sublattice spin-glass model

We study the stability of the replica-symmetric solution of a two-sublattice infinite-range spin-glass model, which can describe the transition from an antiferromagnetic to a spin-glass state. The eigenvalues associated with replica-symmetric perturbations are in general complex. The natural generalization of the usual stability condition is to require the real part of these eigenvalues to be positive. The necessary and sufficient conditions for all the roots of the secular equation to have positive real parts is given by the Hurwitz criterion. The generalized stability condition allows a consistent analysis of the phase diagram within the replica-symmetric approximation.

Tricritical points in the Sherrington-Kirkpatrick model in the presence of discrete random fields

The infinite-range-interaction Ising spin glass is considered in the presence of an external random magnetic field following a trimodal (three-peak) distribution. Such a distribution corresponds to a bimodal added to a probability

The infinite-range two-real-Ising replicas spin glass

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DISPONIBILIDADE E VALOR NUTRITIVO DA VEGETAÇÃO DE CAATINGA NO SEMIÁRIDO NORTE RIOGRANDENSE DO BRASIL

for a field dilution, in such a way that at each site the field

Phase diagrams of the Ashkin-Teller Model on the Cayley Tree

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A EDUCAÇÃO EM MUDANÇAS CLIMÁTICAS: UMA ABORDAGEM INTERDISCIPLINAR

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