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Approach to Fixation for Zero-Temperature Stochastic Ising Models on the Hexagonal Lattice

Authors
  • Camia, Federico
  • Newman, Charles M.
  • Sidoravicius, Vladas
Type
Preprint
Publication Date
Nov 14, 2001
Submission Date
Nov 14, 2001
Identifiers
arXiv ID: math/0111170
Source
arXiv
License
Unknown
External links

Abstract

We investigate zero-temperature dynamics on the hexagonal lattice H for the homogeneous ferromagnetic Ising model with zero external magnetic field and a disordered ferromagnetic Ising model with a positive external magnetic field h. We consider both continuous time (asynchronous) processes and, in the homogeneous case, also discrete time synchronous dynamics (i.e., a deterministic cellular automaton), alternating between two sublattices of H. The state space consists of assignments of -1 or +1 to each site of H, and the processes are zero-temperature limits of stochastic Ising ferromagnets with Glauber dynamics and a random (i.i.d. Bernoulli) spin configuration at time 0. We study the speed of convergence of the configuration $\sigma^t$ at time t to its limit $\sigma^{\infty}$ and related issues.

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