### 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) |
---|---|

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 |

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### ASJC Scopus subject areas

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

### Cite this

*Journal of Physics A: Mathematical and General*,

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

**Zero-temperature dynamics of 2D and 3D Ising ferromagnets.** / Sundaramurthy, Palani; Stein, D. L.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and General*, vol. 38, no. 2, pp. 349-362. https://doi.org/10.1088/0305-4470/38/2/005

}

TY - JOUR

T1 - Zero-temperature dynamics of 2D and 3D Ising ferromagnets

AU - Sundaramurthy, Palani

AU - Stein, D. L.

PY - 2005/1/14

Y1 - 2005/1/14

N2 - We consider zero-temperature, stochastic Ising models σt with nearest-neighbour interactions in two and three dimensions. Using both symmetric and asymmetric initial configurations σ0, we study the evolution of the system with time. We examine the issue of convergence of σt 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.

AB - We consider zero-temperature, stochastic Ising models σt with nearest-neighbour interactions in two and three dimensions. Using both symmetric and asymmetric initial configurations σ0, we study the evolution of the system with time. We examine the issue of convergence of σt 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.

UR - http://www.scopus.com/inward/record.url?scp=11944265512&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=11944265512&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/38/2/005

DO - 10.1088/0305-4470/38/2/005

M3 - Article

VL - 38

SP - 349

EP - 362

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 2

ER -