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Zero-Temperature Dynamics of Plus/Minus J Spin Glasses and Related Models | A. Gandolfi
; C.M. Newman
; D.L. Stein
; | Date: |
19 Oct 2000 | Journal: | Commun. Math. Phys., 214 (2000), 373. | Subject: | Disordered Systems and Neural Networks; Statistical Mechanics; Probability | cond-mat.dis-nn cond-mat.stat-mech math.PR | Affiliation: | Department of Mathematics, University of Rome, Tor Vergata), C.M. Newman (Courant Institute of Mathematical Sciences, New York University), D.L. Stein (Departments of Physics and Mathematics, University of Arizona | Abstract: | We study zero-temperature, stochastic Ising models sigma(t) on a d-dimensional cubic lattice with (disordered) nearest-neighbor couplings independently chosen from a distribution mu on R and an initial spin configuration chosen uniformly at random. Given d, call mu type I (resp., type F) if, for every x in the lattice, sigma(x,t) flips infinitely (resp., only finitely) many times as t goes to infinity (with probability one) --- or else mixed type M. Models of type I and M exhibit a zero-temperature version of ``local non-equilibration’’. For d=1, all types occur and the type of any mu is easy to determine. The main result of this paper is a proof that for d=2, plus/minus J models (where each coupling is independently chosen to be +J with probability alpha and -J with probability 1-alpha) are type M, unlike homogeneous models (type I) or continuous (finite mean) mu’s (type F). We also prove that all other noncontinuous disordered systems are type M for any d greater than or equal to 2. The plus/minus J proof is noteworthy in that it is much less ``local’’ than the other (simpler) proof. Homogeneous and plus/minus J models for d greater than or equal to 3 remain an open problem. | Source: | arXiv, cond-mat/0010296 | Services: | Forum | Review | PDF | Favorites |
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