Abstract
We consider an infinite chain of interacting quantum (anharmonic) oscillators. The pair potential for the oscillators at lattice distanced is proportional to {d 2[log(d+1)]F(d)}−1 where ∑ r∈Z [rF(r)]−1 < ∞. We prove that for any value of the inverse temperatureβ> 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.
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Olivieri, E., Picco, P. & Suhov, Y.M. On the Gibbs states for one-dimensional lattice Boson systems with a long-range interaction. J Stat Phys 70, 985–1028 (1993). https://doi.org/10.1007/BF01053604
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DOI: https://doi.org/10.1007/BF01053604