Carlos S. O. Yokoi

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.

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.

Some exact results for the lattice covering time problem

Abstract The lattice covering time of a random walk in finite lattices has recently been defined as the mean time taken by the lattice walker to visit all the sites of the lattice. We solve the lattice covering time problem exactly in one dimension both for reflecting and periodic boundary conditions.

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.

Elastic Maier-Saupe-Zwanzig model and some properties of nematic elastomers.

We introduce a simple mean-field lattice model to describe the behavior of nematic elastomers. This model combines the Maier-Saupe-Zwanzig approach to liquid crystals and an extension to lattice systems of the Warner-Terentjev theory of elasticity, with the addition of quenched random fields. We use standard techniques of statistical mechanics to obtain analytic solutions for the full range of parameters. Among other results, we show the existence of a stress-strain coexistence curve below a freezing temperature, analogous to the P-V diagram of a simple fluid, with the disorder strength playing the role of temperature. Below a critical value of disorder, the tie lines in this diagram resemble the experimental stress-strain plateau and may be interpreted as signatures of the characteristic polydomain-monodomain transition. Also, in the monodomain case, we show that random fields may soften the first-order transition between nematic and isotropic phases, provided the samples are formed in the nematic state.

Compressible Sherrington–Kirkpatrick spin-glass model

We introduce a Sherrington–Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica method. In the replica-symmetric approximation, we analyze the pressure–temperature phase diagram, and obtain expressions for the critical boundaries between the disordered and the ordered (spin-glass and ferromagnetic) phases. The second-order para–ferromagnetic border ends at a tricritical point, beyond which the transition becomes discontinuous. We use these results to make contact with the temperature–concentration phase diagrams of mixtures of hydrogen-bonded crystals.

Spin 1 ANNNI model with crystal-field anisotropy

In this work we study an axial next-nearest neighbor Ising (ANNNI) model with spin 1 and crystal-field anisotropy. We discuss its properties and construct its phases diagrams within the mean-field approximation. In particular, we show that modulated phases with zero magnetization planes, or partially disordered phases, can be stable for certain range of parameter values.

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.

Chiral Potts model on a Cayley tree with complete and incomplete devil's staircase

The three-state chiral Potts model on a Cayley tree is analysed in the limit of infinitely large coordination number. The fractal dimensionalities of the wavenumber against chiral field curves are computed. It is shown that they change from a complete to an incomplete devils staircase as the temperature is raised. Commensurate phase boundaries are determined analytically for high and low temperatures, and the discommensurations are shown to result from tangent bifurcations.

Monte Carlo study of a spin-1 ANNNI model with single-ion anisotropy

A three-dimensional spin-1 axial next-nearest-neighbor Ising model with single-ion anisotropy is studied using Monte Carlo simulations. The analysis of the thermal effect on the commensurate period six phase shows that it undergoes an internal transition from a low-temperature phase with zero magnetization layers (partially disordered phase) to a high-temperature phase with different symmetry. Results are in good qualitative agreement with previous mean-field studies.