Zero-temperature hysteresis in the random-field Ising model on a Bethe lattice
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In this paper, the authors considered 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.Abstract:
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 , 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.read more
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Phase Transitions and Critical Phenomena
TL;DR: The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results as discussed by the authors, and the major aim of this serial is to provide review articles that can serve as standard references for research workers in the field.
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Exactly solved models in statistical mechanics
TL;DR: In this article, exactly solved models of statistical mechanics are discussed. But they do not consider exactly solvable models in statistical mechanics, which is a special issue in the statistical mechanics of the classical two-dimensional faculty of science.
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Exactly Solved Models in Statistical Mechanics
TL;DR: Baxter has inherited the mantle of Onsager who started the process by solving exactly the two-dimensional Ising model in 1944 as mentioned in this paper, and there has been a growing belief that all the twodimensional lattice statistical models will eventually be solved and that it will be Professor Baxter who solves them.
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Hysteresis and hierarchies: Dynamics of disorder-driven first-order phase transformations.
James P. Sethna,Karin A. Dahmen,Sivan Kartha,James A. Krumhansl,Bruce W. Roberts,Joel D. Shore +5 more
TL;DR: The zero-temperature random-field Ising model is used to study hysteretic behavior at first-order phase transitions using mean-field theory and results of numerical simulations in three dimensions are presented.
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