### Abstract

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 Z^{d}, 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 power). What are the effects of disorder or changes of the lattice? We show that these can quite generally lead to blocking (and convergence to a metastable configuration) even for low d, and then present two examples - one disordered and one homogeneous - where p(t) decays exponentially to p(∞).

Original language | English (US) |
---|---|

Pages (from-to) | 3944-3947 |

Number of pages | 4 |

Journal | Physical Review Letters |

Volume | 82 |

Issue number | 20 |

State | Published - May 17 1999 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physical Review Letters*,

*82*(20), 3944-3947.

**Blocking and persistence in the zero-temperature dynamics of homogeneous and disordered Ising models.** / Newman, Charles; Stein, D. L.

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 82, no. 20, pp. 3944-3947.

}

TY - JOUR

T1 - Blocking and persistence in the zero-temperature dynamics of homogeneous and disordered Ising models

AU - Newman, Charles

AU - Stein, D. L.

PY - 1999/5/17

Y1 - 1999/5/17

N2 - 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 power). What are the effects of disorder or changes of the lattice? We show that these can quite generally lead to blocking (and convergence to a metastable configuration) even for low d, and then present two examples - one disordered and one homogeneous - where p(t) decays exponentially to p(∞).

AB - 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 power). What are the effects of disorder or changes of the lattice? We show that these can quite generally lead to blocking (and convergence to a metastable configuration) even for low d, and then present two examples - one disordered and one homogeneous - where p(t) decays exponentially to p(∞).

UR - http://www.scopus.com/inward/record.url?scp=0000378098&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000378098&partnerID=8YFLogxK

M3 - Article

VL - 82

SP - 3944

EP - 3947

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 20

ER -