Zero-Temperature Dynamics of Ising Spin Systems Following a Deep Quench: Results and Open Problems

Details Zero-Temperature Dynamics of Ising Spin Systems Following a Deep Quench: Results and Open Problems Zero-Temperature Dynamics of Ising Spin Systems Following a Deep Quench: Results and Open Problems

1999-11-22

arxiv.org/abs/cond-mat/9911353v1

Physica A, 279 (2000) 159

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages (LaTeX); to appear in Physica A

Scientific paper

10.1016/S0378-4371(99)00511-7

We consider zero-temperature, stochastic Ising models with nearest-neighbor interactions and an initial spin configuration chosen from a symmetric Bernoulli distribution (corresponding physically to a deep quench). Whether a final state exists, i.e., whether each spin flips only finitely many times as time goes to infinity (for almost every initial spin configuration and realization of the dynamics), or if not, whether every spin - or only a fraction strictly less than one - flips infinitely often, depends on the nature of the couplings, the dimension, and the lattice type. We review results, examine open questions, and discuss related topics.

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