1969: In Journal of Mathematical Physics, 11, 147--154, 1970.

Author: Giovanni Gallavotti, Salvador Miracle--Sole'

Title: Absence of phase transitions in hard core one--dimensional systems with long range interactions

Abstract: We prove the impossibility of phase transitions for a class of infinite range potentials extending recent analogous results. We prove also a cluster property for the equilibrium state $\bar\gamma$ and apply some collateral results to describe, in the case of finite--range interactions, the state $\bar\gamma$ in terms of a family of density distributions, and to verify a general variational property of $\bar\gamma$.

Key words:  Equilibrium Statistical Mechanics, Phase transitions, Long range interactions

Giovanni Gallavotti
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