Zero-Temperature Dynamics of Plus/Minus J Spin Glasses and Related Models

Дата и время публикации : 2000-10-19T19:52:31Z

Авторы публикации и институты :
A. Gandolfi (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)

Ссылка на журнал-издание: Commun. Math. Phys., 214 (2000), 373.
Коментарии к cтатье: 17 pages (RevTeX; 3 figures; to appear in Commun. Math. Phys.)
Первичная категория: cond-mat.dis-nn

Все категории : cond-mat.dis-nn, cond-mat.stat-mech, math.PR

Краткий обзор статьи: 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.

Category: Physics