Convergence in energy-lowering (disordered) stochastic spin systems (Q1863055)

A stochastic finite spin system on the \(d\)-dimensional lattice is considered, in which spin flips do not raise the energy. Earlier results of Nanda-Newman-Stein that each site has almost surely only finitely many flips that strictly lower the energy, and thus that in the models without zero-energy flips there is convergence to an absorbing state, are extended: 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. Results apply to random energy functions with a translation invariant distribution and to general, not necessarily Markovian, dynamics.