## Abstract

We consider stochastic processes, S ^{t} ≡ (S _{x} ^{t}: x ∈ ℤ ^{d}) ∈ script capital L sign _{0} ^{ℤd} with script capital L sign _{0} finite, in which spin flips (i.e., changes of S _{x} ^{t}) do not raise the energy. We extend earlier results of Nanda-Newman-Stein that each site x has almost surely only finitely many flips that strictly lower the energy and thus that in models without zero-energy flips there is convergence to an absorbing state. In particular, the assumption of finite mean energy density can be eliminated by constructing a percolation-theoretic Lyapunov function density as a substitute for the mean energy density. Our results apply to random energy functions with a translation-invariant distribution and to quite general (not necessarily Markovian) dynamics.

Original language | English (US) |
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Pages (from-to) | 431-442 |

Number of pages | 12 |

Journal | Journal of Statistical Physics |

Volume | 110 |

Issue number | 1-2 |

DOIs | |

State | Published - Jan 2003 |

## Keywords

- Absorbing state
- Disordered system
- Energy lowering
- Lyapunov function
- Percolation
- Stochastic Ising model
- Stochastic spin system

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics