# Uniqueness of one-dimensional continuum Gibbs states

Research paper by David Klein

Indexed on: 01 Dec '85Published on: 01 Dec '85Published in: Communications in Mathematical Physics

#### Abstract

We investigate one-dimensional continuum grandcanonical Gibbs states corresponding to finite range superstable many-body potentials. Absence of phase transitions in the sense of uniqueness of the tempered Gibbs state is proved for potentials without hard-core by first proving uniqueness of the Gibbs measures for related hard-core potentials and then taking an appropriate limit of those Gibbs measures.