Hysteresis and avalanches in the T=0 random-field Ising model with 2-spin-flip dynamics (original) (raw)
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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 in the T=0 random-field Ising model: Beyond metastable dynamics
Physical Review E, 2009
We present a numerical study of the zero-temperature response of the Gaussian random-field Ising model (RFIM) to a slowly varying external field, allowing the system to be trapped in microscopic configurations that are not fully metastable. This modification of the standard single-spin-flip dynamics results in an increase of dissipation (hysteresis) somewhat similar to that observed with a finite driving rate. We then study the distribution of avalanches along the hysteresis loop and perform a finite-size scaling analysis that shows good evidence that the critical exponents associated to the disorder-induced phase transition are not modified.
Hysteresis and avalanches in the random anisotropy Ising model
Physical Review B, 2001
The behaviour of the Random Anisotropy Ising model at T=0 under local relaxation dynamics is studied. The model includes a dominant ferromagnetic interaction and assumes an infinite anisotropy at each site along local anisotropy axes which are randomly aligned. Two different random distributions of anisotropy axes have been studied. Both are characterized by a parameter that allows control of the degree of disorder in the system. By using numerical simulations we analyze the hysteresis loop properties and characterize the statistical distribution of avalanches occuring during the metastable evolution of the system driven by an external field. A disorder-induced critical point is found in which the hysteresis loop changes from displaying a typical ferromagnetic magnetization jump to a rather smooth loop exhibiting only tiny avalanches. 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.
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.
Physical Review B, 2003
A numerical study is presented of the third-dimensional Gaussian random-field Ising model at Tϭ0 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 noncritical͒ and two different types of three-dimensional-spanning avalanches ͑critical and subcritical͒, 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.
Numerical approach to metastable states in the zero-temperature random-field Ising model
Physical Review B, 2008
We study numerically the number of single-spin-flip stable states in the T = 0 Random Field Ising Model (RFIM) on random regular graphs of connectivity z = 2 and z = 4 and on the cubic lattice. The annealed and quenched complexities (i.e. the entropy densities) of the metastable states with given magnetization are calculated as a function of the external magnetic field. The results show that the appearance of a (disorder-induced) out-of-equilibrium phase transition in the magnetization hysteresis loop at low disorder can be ascribed to a change in the distribution of the metastable states in the field-magnetization plane.
Diluted three-dimensional random field Ising model at zero temperature with metastable dynamics
Physical Review B, 2006
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.
Hysteresis and avalanches in disordered systems
Journal of Magnetism and Magnetic Materials, 2000
Rate-independent hysteresis is studied in magnetic systems driven by an external "eld for which the in#uence of thermal #uctuations is negligible. In such systems, the hysteresis cycles are not continuous, but rather are composed of a sequence of magnetisation jumps or avalanches between metastable states; the so-called Barkhausen noise. The study of the statistical distribution of such avalanches provides an alternative description to the more common procedure of measuring properties of the loop shape. We focus on four di!erent zero-temperature 3d lattice models: the random "eld Ising model, the random bond Ising model, the site-diluted Ising model and the random anisotropy Ising model. By de"ning appropriate local dynamics, we have studied the metastable evolution by numerical simulations. We analyse the avalanche size distribution as a function of the degree of quenched disorder in these systems. For speci"c amounts of disorder, the distributions exhibit critical behaviour that can be characterised by universal exponents.
The European Physical Journal B, 2006
We present an exact treatment of the hysteresis behavior of the zero-temperature random-field Ising model on a Bethe lattice when it is driven by an external field and evolved according to a 2-spin-flip dynamics. We focus on lattice connectivities z = 2 (the one-dimensional chain) and z = 3. For the latter case, we demonstrate the existence of an out-of-equilibrium phase transition, in contrast with the situation found with the standard 1-spin-flip dynamics. We discuss the influence of the degree of cooperativity of the (local) spin dynamics of the nonequilibrium response on the system.
Zero-temperature hysteresis in the random-field Ising model on a Bethe lattice
Journal of Physics A: Mathematical and General, 1997
We consider the single-spin-flip dynamics of the random-field Ising model on a Bethe lattice at zero temperature in the presence of a uniform external field. We determine the average magnetization as the external field is varied from −∞ to +∞ by setting up the self-consistent field equations, which we show are exact in this case. The qualitative behaviour of magnetization as a function of the external field unexpectedly depends on the coordination number z of the Bethe lattice. For z = 3, with a Gaussian distribution of the quenched random fields, we find no jump in magnetization for any non-zero strength of disorder. For z 4, for weak disorder the magnetization shows a jump discontinuity as a function of the external uniform field, which disappears for a larger variance of the quenched field. We determine exactly the critical point separating smooth hysteresis curves from those with a jump. We have checked our results by Monte Carlo simulations of the model on three-and four-coordinated random graphs, which for large system sizes give the same results as on the Bethe lattice, but avoid surface effects altogether.