Neutron-scattering study of an Ising antiferromagnet above the percolation threshold: Random-field-induced spin-glass-like behavior in Fe0.31Zn0.69F2

Spin-1 Hopfield model under a random field

The goal of the present work is to investigate the role of trivial disorder and nontrivial disorder in the three-state Hopfield model under a Gaussian random field. In order to control the nontrivial disorder, the Hebb interaction is used. This provides a way to control the system frustration by means of the parameter a=p/N, varying from trivial randomness to a highly frustrated regime, in the thermodynamic limit. We performed the thermodynamic analysis using the one-step replica-symmetry-breaking mean field theory to obtain the order parameters and phase diagrams for several strengths of a, the anisotropy constant, and the random field.

Inverse freezing in the Ghatak-Sherrington model with a random field

The present work studies the Ghatak-Sherrington (GS) model in the presence of a magnetic random field (RF). Previous results obtained from the GS model without a RF suggest that disorder and frustration are the key ingredients to produce spontaneous inverse freezing (IF). However, in this model, the effects of disorder and frustration always appear combined. In that sense, the introduction of RF allows us to study the IF under the effects of a disorder which is not a source of frustration. The problem is solved within the one step replica symmetry approximation. The results show that the first order transition between the spin glass and the paramagnetic phases, which is related to the IF for a certain range of crystal field D, is gradually suppressed when the RF is increased.

Ising spin glass under continuous-distribution random magnetic fields: Tricritical points and instability lines

The effects of random magnetic fields are considered in an Ising spin-glass model defined in the limit of infinite-range interactions. The probability distribution for the random magnetic fields is a double Gaussian, which consists of two Gaussian distributions centered, respectively, at +H0 and -H0, presenting the same width sigma . It is argued that such a distribution is more appropriate for a theoretical description of real systems than its simpler particular two well-known limits, namely, the single Gaussian distribution (sigma>>H0) and the bimodal one (sigma=0) . The model is investigated by means of the replica method, and phase diagrams are obtained within the replica-symmetric solution. Critical frontiers exhibiting tricritical points occur for different values of sigma , with the possibility of two tricritical points along the same critical frontier. To our knowledge, it is the first time that such a behavior is verified for a spin-glass model in the presence of a continuous-distribution random field, which represents a typical situation of a real system. The stability of the replica-symmetric solution is analyzed, and the usual Almeida-Thouless instability is verified for low temperatures. It is verified that the higher-temperature tricritical point always appears in the region of stability of the replica-symmetric solution; a condition involving the parameters H0 and sigma , for the occurrence of this tricritical point only, is obtained analytically. Some of our results are discussed in view of experimental measurements available in the literature.

Microscopic description of an Ising spin glass near the percolation threshold

Monte Carlo results using a microscopic model to describe FexZn(1-x)F2 indicate that its spin-glass phase at x=0.25 and zero magnetic field is characterized by the presence of antiferromagnetic fractal domains, separated by random vacancies and strongly correlated in time. The effective local random-field distribution corroborates this glassy behavior, which emerges irrespective of ab initio competing interactions and is a consequence of the fractal domain structure near the percolation threshold, x(p)=0.24. The aging properties of the system are in agreement with predictions of short-range stochastic spin-glass models and with the droplets model for spin glass close to percolation.

Effects of random fields in an antiferromagnetic Ising spin glass

The effects of random fields on the two-sublattice infinite-ranged Ising spin-glass model are investigated. This model is expected to be appropriate as a mean-field description of antiferromagnetic spin glasses such as FexMn1-xTiO3. Within replica-symmetric calculations, we study the influence of Gaussian and bimodal random fields on the phase transitions and phase diagrams. It is shown that, in the presence of random fields, the first-order transitions are weakened and may become continuous. Also, the antiferromagnetic phases are always destroyed by sufficiently strong random fields. A qualitative comparison with existing experimental results and the limitations of the present calculations are discussed.