Equilibrium pure states and nonequilibrium chaos

Journal Article · Mon Feb 01 04:00:00 EST 1999 · Journal of Statistical Physics

OSTI ID:343659

Newman, C M ^[1]; Stein, D L ^[2]

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1. New York Univ., NY (United States). Courant Inst. of Mathematical Sciences
2. Univ. of Arizona, Tucson, AZ (United States)

The authors consider nonequilibrium systems such as the Edwards-Anderson Ising spin glass at a temperature where, in equilibrium, there are presumed to be (two or many) broken-symmetry pure states. Following a deep quench, they argue that as time t {r_arrow} {infinity}, although the system is usually in some pure state locally, either it never settles permanently on a fixed length scale into a single pure state, or it does, but then the pure state depends on both the initial spin configuration and the realization of the stochastic dynamics. But this latter case can occur only if there exists an uncountable number of pure states (for each coupling realization) with almost every pair having zero overlap. In both cases, almost no initial spin configuration is in the basin of attraction of a single pure state; that is, the configuration space (resulting from a deep quench) is all boundary (except for a set of measure zero). They prove that the former case holds for deeply quenched 2D ferromagnets. Their results raise the possibility that even if more than one pure state exists for an infinite system, time averages do not necessarily disagree with Boltzmann averages.

• Sponsoring Organization: National Science Foundation, Washington, DC (United States); USDOE, Washington, DC (United States)
• DOE Contract Number: FG03-93ER25155
• OSTI ID: 343659
• Journal Information: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 3-4 Vol. 94; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DYNAMICS
ERGODIC HYPOTHESIS
FERROMAGNETIC MATERIALS
ISING MODEL
QUENCHING
SPIN GLASS STATE
STATISTICAL MECHANICS
STOCHASTIC PROCESSES