Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

The Gibbs free energy of formation of a glass alloy

A simple expression for the Gibbs free energy of formation of a pure component or a eutectic alloy glass, relative to the stable crystalline phase (or phases) at the same temperature is deduced by use of thermodynamic arguments. The expression obtained is supposed to apply to both monocomponent and multicomponent liquid alloys that might become glasses from the supercooled liquid state, irrespective of the critical cooling rate needed to avoid crystallization.

Slow Dynamics of Ising Models with Energy Barriers

Using Monte Carlo simulations we study the dynamics of three-dimensional Ising models with nearest-, next-nearest-, and four-spin (plaquette) interactions. During coarsening, such models develop growing energy barriers, which leads to very slow dynamics at low temperature. As already reported, the model with only the plaquette interaction exhibits some of the features characteristic of ordinary glasses: strong metastability of the supercooled liquid, a weak increase of the characteristic length under cooling, stretched-exponential relaxation, and aging. The addition of two-spin interactions, in general, destroys such behavior: the liquid phase loses metastability and the slow-dynamics regime terminates well below the melting transition, which is presumably related with a certain corner-rounding transition. However, for a particular choice of interaction constants, when the ground state is strongly degenerate, our simulations suggest that the slow-dynamics regime extends up to the melting transition. The analysis of these models leads us to the conjecture that in the four-spin Ising model domain walls lose their tension at the glassy transition and that they are basically tensionless in the glassy phase.

Fragile-glass behavior of a short-range p-spin model

We propose a short-range generalization of the p-spin interaction spin-glass model. The model is well suited to test the idea that an entropy collapse is at the bottom line of the dynamical singularity encountered in structural glasses. The model is studied in three dimensions through Monte Carlo simulations, which put in evidence fragile glass behavior with stretched exponential relaxation and super-Arrhenius behavior of the relaxation time. Our data are in favor of a Vogel-Fulcher behavior of the relaxation time, related to an entropy collapse at the Kauzmann temperature. We, however, encounter difficulties analogous to those found in experimental systems when extrapolating thermodynamical data at low temperatures. We study the spin-glass susceptibility, investigating the behavior of the correlation length in the system. We find that the increase of the relaxation time is accompanied by a very slow growth of the correlation length. We discuss the scaling properties of off-equilibrium dynamics in the glassy regime, finding qualitative agreement with the mean-field theory.

Erasing the glassy state in magnetic fine particles

BaFe10.4Co0.8Ti0.8O19 magnetic fine particles exhibit most of the features attributed to glassy behavior, e.g., irreversibility in the hysteresis loops and in the zero-field-cooling and field-cooling curves extends up to very high fields, and aging and magnetic training phenomena occur. However, the multivalley energy structure of the glassy state can be strongly modified by a field-cooling process at a moderate field. Slow relaxation experiments demonstrate that the intrinsic energy barriers of the individual particles dominate the behavior of the system at high cooling fields, while the energy states corresponding to collective glassy behavior play the dominant role at low cooling fields.

Reply to "Comment on 'Erasing glassy state in magnetic fine particles'"

The Comment affirms that no phase transition occurs in spin-glass systems with an applied magnetic field. However, only according to the droplet model is this result expected. Other models do not predict this result and, consequently, it is under current discussion. In addition, we show how the experimental results obtained in our system correspond to a cluster glass rather than to a true spin glass.

Squared interaction matrix Sherrington-Kirkpatrick model for a spin glass

The mean-field theory of a spin glass with a specific form of nearest- and next-nearest-neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we find either the continuous replica symmetry breaking seen in the Sherrington-Kirkpartick model or a one-step solution similar to that found in structural glasses. Our results are confirmed by numerical simulations and the link between the type of spin-glass behavior and the density of eigenvalues of the interaction matrix is discussed.

General method to determine replica symmetry breaking transitions

We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character of the spin-glass order parameter. This new parameter can be used to study models with time reversal symmetry but its greatest interest lies in models where this symmetry is absent. We apply the method to long-range and short-range Ising spin-glasses with and without a magnetic field as well as short-range multispin interaction spin-glasses.

Glassiness in a model without energy barriers

We propose a microscopic model without energy barriers in order to explain some generic features observed in structural glasses. The statics can be exactly solved while the dynamics has been clarified using Monte Carlo calculations. Although the model has no thermodynamic transition, it captures some of the essential features of real glasses, i.e., extremely slow relaxation, time dependent hysteresis effects, anomalous increase of the relaxation time, and aging. This suggests that the effect of entropy barriers can be an important ingredient to account for the behavior observed in real glasses.

Spin-glass behaviour in mixed metal oxides with a rutile-type structure

We report here on the magnetic properties of compounds of composition Fe1−xCrxSbO4 and Fe1−xGaxSbO4. The introduction of paramagnetic Cr3+ and diamagnetic Ga3+ into the rutile‐related iron antimonate lattice does not destroy the antisite atomic ordering which exists in iron antimonate of composition FeSbO4. The initial slope of the Curie temperature dependence on x is similar in both series, indicating that Fe3+‐Cr3+ interactions are very small. The magnetic susceptibility measurements recorded from the compounds of composition Fe1−xCrxSbO4, x<0.4, and Fe0.9Ga0.1SbO4 show them to behave as spin glasses at low temperatures. The inhibition of compounds of the type Fe1−xCrxSbO4, x>0.4, and Fe1−xGaxSbO4, x>0.1 to undergo a spin‐glass transition above 4.2 K is associated with a dilution effect.