Metastability in zero-temperature dynamics: Statistics of attractors

Details Metastability in zero-temperature dynamics: Statistics of attractors Metastability in zero-temperature dynamics: Statistics of attractors

2004-12-03

arxiv.org/abs/cond-mat/0412077v1

J. Phys. Cond. Matt. 17, S2573-S2590 (2005)

Physics

Condensed Matter

Statistical Mechanics

21 pages, 6 figures. To appear in special issue of JPCM on Granular Matter edited by M. Nicodemi

Scientific paper

10.1088/0953-8984/17/24/014

The zero-temperature dynamics of simple models such as Ising ferromagnets provides, as an alternative to the mean-field situation, interesting examples of dynamical systems with many attractors (absorbing configurations, blocked configurations, zero-temperature metastable states). After a brief review of metastability in the mean-field ferromagnet and of the droplet picture, we focus our attention onto zero-temperature single-spin-flip dynamics of ferromagnetic Ising models. The situations leading to metastability are characterized. The statistics and the spatial structure of the attractors thus obtained are investigated, and put in perspective with uniform a priori ensembles. We review the vast amount of exact results available in one dimension, and present original results on the square and honeycomb lattices.

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