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

Abstract

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.

10 pages (LaTeX); to appear in Physica A

References in corpus (3)

• Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models
• Metastable States in Spin Glasses and Disordered Ferromagnets
• Zero-Temperature Dynamics of Plus/Minus J Spin Glasses and Related Models

Cited by in corpus (10)

• Fate of Zero-Temperature Ising Ferromagnets
• Zero-Temperature Relaxation of Three-Dimensional Ising Ferromagnets
• Metastability in zero-temperature dynamics: Statistics of attractors
• Zero Temperature Dynamics of 2D and 3D Ising Ferromagnets
• Zero-temperature dynamics in the dilute Curie-Weiss model
• The Percolation Transition in the Zero-Temperature Domany Model
• Persistence and the Random Bond Ising Model in Two Dimensions
• Anomalous Ising freezing times
• Time decay of the remanent magnetization in the $\pm J$ spin glass model at T=0
• Zero Temperature Dynamics of Ising Systems on Hypercubes