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We analyze the demagnetization properties of the random-field Ising model on the Bethe lattice focusing on the beahvior near the disorder induced phase transition. We derive an exact recursion relation for the magnetization and integrate it numerically. Our analysis shows that demagnetization is possible only in the continous high disorder phase, where at low field the loops are described by the Rayleigh law. In the low disorder phase, the saturation loop displays a discontinuity which is reflected by a non vanishing magnetization m_\infty after a series of nested loops. In this case, at low fields the loops are not symmetric and the Rayleigh law does not hold.Comment: 8pages, 6 figure

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“…16 and 17, the generalization of the results is streightforward but lenghty as discussed, for instance, in Ref. 21.…”

Section: Introductionmentioning

confidence: 87%

Rayleigh loops in the random-field Ising model on the Bethe lattice

2002

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“…6 For a finite system of size N, an avalanche then occurs in the interval dH with a rate dP / dH = NG͑H͒ ͓recall that G͑H͒dH, as calculated in Ref. 9, is a probability per spin͔. The mean range of stability ͗⌬H͘ H of a metastable state before an avalanche occurs is given by the inverse of the rate, i.e.,…”

Section: A Fraction Of Stable States Along the H-driven And M-drivenmentioning

confidence: 99%

“…This is to benefit from the fact that an almost complete analytical description is available in the fielddriven case. [8][9][10] Comparing our simulation data with these exact results will help in understanding the similarities and differences between the two protocols.…”

Section: Introductionmentioning

confidence: 96%

Magnetization-driven random-field Ising model atT=0

et al. 2006

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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.

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“…6,7 Moreover, many properties of the critical point have also been studied analytically on Bethe lattices. [8][9][10][11][12] Experimental evidence for the occurrence of such a critical point has been found in different magnetic systems. 13,14 Another interesting result of the RFIM with metastable dynamics is that it reproduces the experimental observation that m͑H͒ trajectories of such athermal systems are discontinuous on small scales.…”

Section: Introductionmentioning

confidence: 99%

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

Illa

Vives

2006

Phys. Rev. B

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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.

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Cited by 46 publications

References 16 publications

Rayleigh loops in the random-field Ising model on the Bethe lattice

Rayleigh loops in the random-field Ising model on the Bethe lattice

Magnetization-driven random-field Ising model atT=0

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

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