Stationary Properties of a Randomly Driven Ising Ferromagnet (original) (raw)
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The randomly driven Ising ferromagnet: I. General formalism and mean-field theory
Journal of Physics A: Mathematical and General, 1999
We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast switching, random external field. After introducing a general formalism for describing such systems, we consider here the mean-field theory. A novel type of first order phase transition related to spontaneous symmetry breaking and dynamic freezing is found. The non-equilibrium stationary state has a complex structure, which changes as a function of parameters from a singular-continuous distribution with Euclidean or fractal support to an absolutely continuous one. These transitions are reflected in both finite size effects and sample-to-sample fluctuations. PACS numbers: 05.50+g 05.70.Jk 64.60Cn 68.35.Rh 75.10.H 82.20.M
Statistical Mechanics of Strongly Driven Ising Systems
This work considers the behavior the Ising model of a ferromagnet subject to a strong, randomly switching external driving field. A formalism based on the master equation to handle such nonequilibrium systems is introduced and applied to a mean field approximation, and one- and two-dimensional variants of the model. A novel type of phase transition related to spontaneous symmetry breaking and dynamic freezing occurs which depends on the strength of the driving field. The complex analytic structure of the stationary magnetization distributions is shown to range from singular-continuous with euclidean or fractal support to all continuous. Analytic results are presented for the mean field and one-dimensional cases, whereas Monte-Carlo simulations provide insight into the two-dimensional model. Also, an interpretation of the model from a neurobiological point of view is given.
Magnetization-driven random-field Ising model at T=0
Physical Review B, 2006
We study the hysteretic evolution of the random field Ising model at T = 0 when the magnetization M is controlled externally and the magnetic field H becomes the output variable. The dynamics is a simple modification of the single-spin-flip dynamics used in the H-driven situation and consists in flipping successively the spins with the largest local field. This allows one to perform a detailed comparison between the microscopic trajectories followed by the system with the two protocols. Simulations are performed on random graphs with connectivity z =4 ͑Bethe lattice͒ and on the three-dimensional cubic lattice. The same internal energy U͑M͒ is found with the two protocols when there is no macroscopic avalanche and it does not depend on whether the microscopic states are stable or not. On the Bethe lattice, the energy inside the macroscopic avalanche also coincides with the one that is computed analytically with the H-driven algorithm along the unstable branch of the hysteresis loop. The output field, defined here as ⌬U / ⌬M, exhibits very large fluctuations with the magnetization and is not self-averaging. The relation to the experimental situation is discussed.
The randomly driven Ising ferromagnet: II. One and two dimensions
Journal of Physics A: Mathematical and General, 1999
We consider the behaviour of an Ising ferromagnet obeying the Glauber dynamics under the influence of a fast-switching, random external field. In paper I, we introduced a general formalism for describing such systems and presented the mean-field theory. In this article we derive results for the one-dimensional case, which can be only partially solved. Monte Carlo simulations performed on a square lattice indicate that the main features of the mean-field theory survive the presence of strong fluctuations.
2006
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 thermallly activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model (RFIM) 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 re-entrant 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...
Hysteresis and avalanches in the T=0 random-field Ising model with two-spin-flip dynamics
Physical Review B, 2005
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, historydependent 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 size͒ 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.
Hysteresis and avalanches in the T=0 random-field Ising model with 2-spin-flip dynamics
2004
We study the non-equilibrium behavior of the three-dimensional Gaussian random-field Ising model at T=0 in the presence of a uniform external field using a 2-spin-flip dynamics. The deterministic, history-dependent evolution of the system is compared with the one obtained with the standard 1-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.
Generalized off-equilibrium fluctuation-dissipation relations in random Ising systems
The European Physical Journal B, 1999
We show that the numerical method based on the off-equilibrium fluctuation-dissipation relation does work and is very useful and powerful in the study of disordered systems which show a very slow dynamics. We have verified that it gives the right information in the known cases (diluted ferromagnets and random field Ising model far from the critical point) and we used it to obtain more convincing results on the frozen phase of finite-dimensional spin glasses. Moreover we used it to study the Griffiths phase of the diluted and the random field Ising models.
Dynamical properties of random-field Ising model
Physical Review E, 2013
Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter and the spin-spin correlation functions are studied in the non equilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that for weak random fields, the two dimensional random field Ising model possesses long range order. Except for weak disorder, exchange interaction never wins over pinning interaction to establish long range order in the system.
Theory of the Random Field Ising Model
Series on Directions in Condensed Matter Physics, 1997
A review is given on some recent developments in the theory of the Ising model in a random field. This model is a good representation of a large number of impure materials. After a short repetition of earlier arguments, which prove the absence of ferromagnetic order in d ≤ 2 space dimensions for uncorrelated random fields, we consider different random field correlations and in particular the generation of uncorrelated from anti-correlated random fields by thermal fluctuations. In discussing the phase transition, we consider the transition to be characterized by a divergent correlation length and compare the critical exponents obtained from various methods (real space RNG, Monte Carlo calculations, weighted mean field theory etc.). The ferromagnetic transition is believed to be preceded by a spin glass transition which manifests itself by replica symmetry breaking. In the discussion of dynamical properties, we concentrate mainly on the zero temperature depinning transition of a domain wall, which represents a critical point far from equilibrium with new scaling relations and critical exponents.