Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models

Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models

A “persistence” exponent θ has been extensively used to describe the nonequilibrium dynamics of spin systems following a deep quench: for zero-temperature homogeneous Ising models on the d-dimensional cubic lattice Zd, the fraction p(t) of spins not flipped by time t decays to zero like t−θ(d) for low d; for high d, p(t) may decay to p(∞) > 0, because of “blocking” (but perhaps still like a pow...

Zero Temperature Dynamics of the Weakly-disordered Ising Model

The Glauber dynamics of the pure and weakly-disordered random-bond 2d Ising model is studied at zero-temperature. The coarsening length scale, L(t), is extracted from the equal time correlation function. In the pure case, the persistence probability decreases algebraically with L(t). In the disordered case, three distinct regimes are identified: a short time regime where the behaviour is pure-l...

1 7 Ju n 19 99 Persistence in the Zero - Temperature Dynamics of the Disordered Ising Model

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

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 aut...

Zero-Temperature Dynamics of ± J Spin Glasses and Related Models

We study zero-temperature, stochastic Ising models σ on Z with (disordered) nearest-neighbor couplings independently chosen from a distribution μ on R and an initial spin configuration chosen uniformly at random. Given d, call μ type I (resp., type F) if, for every x in Z, σ x flips infinitely (resp., only finitely) many times as t → ∞ (with probability one) — or else mixed type M. Models of ty...