The Life of Amoebas (of the Ising Model)

S. Shlosman

2001, v.7, Issue 1, 113-115

ABSTRACT

This is an extended abstract of my paper Path Large Deviations and Other Typical Properties of the Low-Temperature Models, with Applications to the Weakly Gibbs States, which have appeared in [S. Shlosman, Path Large Deviations and Other Typical Properties of the Low-Temperature Models, with Applications to the Weakly Gibbs States, Markov Processes Relat. Fields, 2000, v.6, pp.121-133]. In it I have established a new property of typical configurations of the low temperature pure phases of the lattice models satisfying the conditions of Pirogov - Sinai theory. This property is called the Amoeba Property. Its typicality allows me to extend the range of the validity of the Weakly Gibbs property of the random fields. Namely, I prove that the marginals of Gibbs fields are Weakly Gibbs fields.

Keywords: large deviations,typical property,weakly Gibbs state,quenchedcorrelation decay

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