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

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

2001-11-14

arxiv.org/abs/math/0111170v1

Mathematics

Probability

20 pages, to appear in "In and out of equilibrium: probability with a physics flavor", Progress in Probability, Birkhauser

Scientific paper

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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