Zero-temperature dynamics of the weakly disordered Ising model

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...

Zero-Temperature Stochastic Ising Model

We analyze clustering and (local) recurrence of a standard Markov process model of spatial domain coarsening. The continuous time process, whose state space consists of assignments of +1 or −1 to each site in Z, is the zero-temperature limit of the stochastic homogeneous Ising ferromagnet (with Glauber dynamics): the initial state is chosen uniformly at random and then each site, at rate one, p...

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...

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

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