Comparison between molecular dynamics abd Monte Carlo simulations of an ordering process in a binary alloy

Ordering in a binary alloy is studied by means of a molecular-dynamics (MD) algorithm which allows to reach the domain growth regime. Results are compared with Monte Carlo simulations using a realistic vacancy-atom (MC-VA) mechanism. At low temperatures fast growth with a dynamical exponent x>1/2 is found for MD and MC-VA. The study of a nonequilibrium ordering process with the two methods shows the importance of the nonhomogeneity of the excitations in the system for determining its macroscopic kinetics.

Magnetic phase separation in ordered alloys

We present a lattice model to study the equilibrium phase diagram of ordered alloys with one magnetic component that exhibits a low temperature phase separation between paramagnetic and ferromagnetic phases. The model is constructed from the experimental facts observed in Cu3-xAlMnx and it includes coupling between configurational and magnetic degrees of freedom that are appropriate for reproducing the low temperature miscibility gap. The essential ingredient for the occurrence of such a coexistence region is the development of ferromagnetic order induced by the long-range atomic order of the magnetic component. A comparative study of both mean-field and Monte Carlo solutions is presented. Moreover, the model may enable the study of the structure of ferromagnetic domains embedded in the nonmagnetic matrix. This is relevant in relation to phenomena such as magnetoresistance and paramagnetism

Hysteresis and avalanches in the random anisotropy Ising model

ches. The critical point is characterized by a set of critical exponents, which are consistent with the universal values proposed from the study of other simpler models.

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.

Disorder-induced critical phenomena in magnetically glassy Cu-Al-Mn alloys

Measurements of magnetic hysteresis loops in Cu-Al-Mn alloys of different Mn content at low temperatures are presented. The loops are smooth and continuous above a certain temperature, but exhibit a magnetization discontinuity below that temperature. Scaling analysis suggest that this system displays a disorder-induced phase transition line. Measurements allow one to determine the critical exponents ß=0.03±0.01 and ß¿=0.4±0.1, which coincide with those reported recently in a different system, thus supporting the existence of universality for disorder-induced critical points.

Kinetics of martensitic transitions in Cu-Al-Mn under thermal cycling: Analysis at multiple length scales

In this paper we study the evolution of the kinetic features of the martensitic transition in a Cu-Al-Mn single crystal under thermal cycling. The use of several experimental techniques including optical microscopy, calorimetry, and acoustic emission, has enabled us to perform an analysis at multiple scales. In particular, we have focused on the analysis of avalanche events (associated with the nucleation and growth of martensitic domains), which occur during the transition. There are significant differences between the kinetics at large and small length scales. On the one hand, at small length scales, small avalanche events tend to sum to give new larger events in subsequent loops. On the other hand, at large length scales the large domains tend to split into smaller ones on thermal cycling. We suggest that such different behavior is the necessary ingredient that leads the system to the final critical state corresponding to a power-law distribution of avalanches.

Spanning avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics: Field dependence and geometrical properties

Spanning avalanches in the 3D Gaussian Random Field Ising Model (3D-GRFIM) with metastable dynamics at T=0 have been studied. Statistical analysis of the field values for which avalanches occur has enabled a Finite-Size Scaling (FSS) study of the avalanche density to be performed. Furthermore, a direct measurement of the geometrical properties of the avalanches has confirmed an earlier hypothesis that several types of spanning avalanches with two different fractal dimensions coexist at the critical point. We finally compare the phase diagram of the 3D-GRFIM with metastable dynamics with the same model in equilibrium at T=0.

Hysteresis and avalanches in the T=0 random field ising model with 2-spin flip dynamics

We study the nonequilibrium behavior of the three-dimensional Gaussian random-field Ising model at T=0 in the presence of a uniform external field using a two-spin-flip dynamics. The deterministic, history-dependent evolution of the system is compared with the one obtained with the standard one-spin-flip dynamics used in previous studies of the model. The change in the dynamics yields a significant suppression of coercivity, but the distribution of avalanches (in number and size) stays remarkably similar, except for the largest ones that are responsible for the jump in the saturation magnetization curve at low disorder in the thermodynamic limit. By performing a finite-size scaling study, we find strong evidence that the change in the dynamics does not modify the universality class of the disorder-induced phase transition.

Diluted three-dimensional random field Ising model at zero temperature with metastable dynamics.

The influence of vacancy concentration on the behavior of the three-dimensional random field Ising model with metastable dynamics is studied. We have focused our analysis on the number of spanning avalanches which allows us a clear determination of the critical line where the hysteresis loops change from continuous to discontinuous. By a detailed finite-size scaling analysis we determine the phase diagram and numerically estimate the critical exponents along the whole critical line. Finally, we discuss the origin of the curvature of the critical line at high vacancy concentration.

Influence of the driving mechanism on the response of systems with athermal dynamics: The example of the random-field Ising model

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local mean-field theory at finite temperature (but neglecting thermally activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model when controlling either the external magnetic field H or the extensive magnetization M. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the H-driven and M-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the H-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the M-driven loop is reentrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.