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On the Gibbs states for one-dimensional lattice Boson systems with a long-range interaction |
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| Authors: | E Olivieri P Picco Yu M Suhov |
| Institution: | (1) Dipartimento di Matematica, Università di Roma  Tor Vergata, , Rome, Italy;(2) Centre de Physique Théorique, CNRS-Luminy, Marseille, France;(3) Institute for Problems of Information Transmission, Russian Academy of sciences, Moscow, Russia;(4) Dipartimento di Matematica Guido Castelnuovo,, Università degli Studi di Roma La Sapienza,, Rome, Italy;(5) Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, England;(6) Courant Institute of Mathematical Sciences, New York, New York |
| Abstract: | We consider an infinite chain of interacting quantum (anharmonic) oscillators. The pair potential for the oscillators at lattice distanced is proportional to {d
2log(d+1)]F(d)}–1 where 
r Z rF(r)]–1 <  . We prove that for any value of the inverse temperature > 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. |
| Keywords: | Quantum systems Gibbs states |
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