### Abstract

We consider zero-temperature, stochastic Ising models σ^{t} with nearest-neighbour interactions in two and three dimensions. Using both symmetric and asymmetric initial configurations σ^{0}, we study the evolution of the system with time. We examine the issue of convergence of σ^{t} and discuss the nature of the final state of the system. By determining a relation between the median number of spin flips per site ν, the probability p that a spin in the initial spin configuration takes the value +1, and lattice size L, we conclude that in two and three dimensions, the system converges to a frozen (but not necessarily uniform) state when p ≠ 1/2. Results for p = 1/2 in three dimensions are consistent with the conjecture that the system does not evolve towards a fully frozen limiting state. Our simulations also uncover 'striped' and 'blinker' states first discussed by Spirin et al (2001 Phys. Rev. E 63 036118), and their statistical properties are investigated.

Original language | English (US) |
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Pages (from-to) | 349-362 |

Number of pages | 14 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 38 |

Issue number | 2 |

DOIs | |

State | Published - Jan 14 2005 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)

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## Cite this

*Journal of Physics A: Mathematical and General*,

*38*(2), 349-362. https://doi.org/10.1088/0305-4470/38/2/005