Abstract
We consider stochastic processes, St ≡ (Sx t: x ∈ ℤd) ∈ script capital L sign 0ℤd with script capital L sign0 finite, in which spin flips (i.e., changes of Sxt) 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