Abstract
We consider Ising spin systems, equivalently lattice gases evolving under discrete- or continuous-time Markov processes, i.e., “stochastic cellular automata” or “interacting particle systems.” We show that for certain spin-flip probabilities or rates and suitable initial states the expectation values of products of spin variables taken at equal or different times are nonnegative; they satisfy the same inequalities as the equal-time correlations of ferromagnetic systems in equilibrium (first Griffiths inequality). Extensions of FKG inequalities to time-displaced correlations are also discussed.
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Ferrari, P.A., Lebowitz, J.L. & Maes, C. On the positivity of correlations in nonequilibrium spin systems. J Stat Phys 53, 295–305 (1988). https://doi.org/10.1007/BF01011558
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DOI: https://doi.org/10.1007/BF01011558