Convergence in Energy-Lowering (Disordered) Stochastic Spin Systems

Emilio De Santis, Charles M. Newman

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)431-442
Number of pages12
JournalJournal of Statistical Physics
Volume110
Issue number1-2
DOIs
StatePublished - 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

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