Metastable States in Spin Glasses and Disordered Ferromagnets

Details Metastable States in Spin Glasses and Disordered Ferromagnets Metastable States in Spin Glasses and Disordered Ferromagnets

1999-08-30

arxiv.org/abs/cond-mat/9908455v1

Phys. Rev. E, 60 (1999) 5244

Physics

Condensed Matter

Disordered Systems and Neural Networks

34 pages (LaTeX); to appear in Physical Review E

Scientific paper

10.1103/PhysRevE.60.5244

We study analytically M-spin-flip stable states in disordered short-ranged Ising models (spin glasses and ferromagnets) in all dimensions and for all M. Our approach is primarily dynamical and is based on the convergence of a zero-temperature dynamical process with flips of lattice animals up to size M and starting from a deep quench, to a metastable limit. The results (rigorous and nonrigorous, in infinite and finite volumes) concern many aspects of metastable states: their numbers, basins of attraction, energy densities, overlaps, remanent magnetizations and relations to thermodynamic states. For example, we show that their overlap distribution is a delta-function at zero. We also define a dynamics for M=infinity, which provides a potential tool for investigating ground state structure.

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