Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
1998-09-28
J. Stat. Phys., 94 (1999) 709
Physics
Condensed Matter
Disordered Systems and Neural Networks
13 pages (LaTeX); to appear in Journal of Statistical Physics
Scientific paper
We 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, we argue that as time goes to infinity, although the system is usually in some pure state locally, either it never settles permanently on a fixed lengthscale 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). We prove that the former case holds for deeply quenched two-dimensional ferromagnets. Our results raise the possibility that even if more than one pure state exists for an infinite system, time averages don't necessarily disagree with Boltzmann averages.
Newman Charles M.
Stein Daniel L.
No associations
LandOfFree
Equilibrium Pure States and Nonequilibrium Chaos does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Equilibrium Pure States and Nonequilibrium Chaos, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equilibrium Pure States and Nonequilibrium Chaos will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-481966