Journal Article10.1103/PHYSREVLETT.49.409
Classical Spin-Glass Model
143
TL;DR: In this paper, a simple model of a spin-glass with weakly correlated disorder is presented, which includes both randomness and frustration, and is exactly soluble, but its solution can be obtained without replicas.
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Abstract: A simple model of a classical spin-glass with weakly correlated disorder is presented. It includes both randomness and frustration, and is exactly soluble, but its solution can be obtained without replicas. Among the several phases of the model a mixed phase is found where spin-glass and ferromagnetism coexist. In addition the characteristic S shape of the spin-glass magnetization is reproduced.
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Citations
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Ergodicity of the Coupling Constants and the Symmetric n -Replicas Trick for a Class of Mean-Field Spin-Glass Models
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References
Introduction to Phase Transitions and Critical Phenomena
H. Eugene Stanley,Victor K. Wong +1 more
TL;DR: In this article, the authors present a paperback edition of a distinguished book, originally published by Clarendon Press in 1971, which is at the level at which a graduate student who has studied condensed matter physics can begin to comprehend the nature of phase transitions, which involve the transformation of one state of matter into another.
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Solvable Model of a Spin-Glass
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TL;DR: The stationary point used by Sherrington and Kirkpatrick (1975) in their evaluation of the free energy of a spin glass by the method of steepest descent is examined carefully in this article, and it is found that although this point is a maximum of the integrand at high temperatures, it is not a maximum in the spin glass phase nor in the ferromagnetic phase at low temperatures.