On the absence of phase transition in one-dimensional random fields
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Sufficient conditions are given for a one-dimensional random field specification (system of conditional distributions) to admit at most one unconditional distribution within a specified class of such distributions. The proof of the main result is based on a limit theorem on the asymptotic behaviour of the specification in relation to the field, which expresses the weak dependence of the conditional distributions on distant sites. In a subsequent article the results are applied to a class of superstable spin systems with long range interaction.
KeywordsPhase Transition Probability Measure Random Field Conditional Distribution Tame
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