ON THE GIBBS STATES FOR ONE-DIMENSIONAL LATTICE BOSON SYSTEMS WITH A LONG-RANGE INTERACTION E. Olivieri

Abstract

: We consider an infinite chain of interacting quantum (anharmonic) oscillators. The pair potential for the oscillators at lattice distance d is proportional to (d 2 (log(d + 1))F (d)) Gamma1 where Sigma r2Z (rF (r)) Gamma1 ! 1. We prove that for any value of the inverse temperature fi ? 0 there exists a limiting Gibbs state which is translationally invariant and ergodic. Furthermore, it is analytic in a natural sense. This shows the absence of phase transitions in the systems under consideration for any value of the thermodynamic parameters. February 1992 1 Dipartimento di Matematica, Universit'a di Roma "Tor Vergata", Roma ITALIA.CNR-GNFM. 2 Centre de Physique Th'eorique, CNRS-Luminy, Marseille FRANCE. 3 Institute for Problems of Information Transmission, The Russian Academy of Sciences, Moscow RUSSIA. 4 Dipartimento di Matematica "Guido Castelnuovo", Universit'a degli Studi di Roma "La Sapienza", Roma ITALIA. 5 Statistical Laboratory, Department of Pure Mathematics and Mat...