Convergence in Energy-Lowering (Disordered) Stochastic Spin Systems

Emilio De Santis, Charles Newman

Research output: Contribution to journalArticle

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

Fingerprint

Spin Systems
Flip
Stochastic Systems
Energy Density
Energy
Invariant Distribution
flux density
Random Function
Substitute
Energy Function
Absorbing
Liapunov functions
Lyapunov Function
energy
Stochastic Processes
stochastic processes
Strictly
Zero
substitutes
Model

Keywords

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

ASJC Scopus subject areas

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

Cite this

Convergence in Energy-Lowering (Disordered) Stochastic Spin Systems. / De Santis, Emilio; Newman, Charles.

In: Journal of Statistical Physics, Vol. 110, No. 1-2, 01.2003, p. 431-442.

Research output: Contribution to journalArticle

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