Abstract
We consider an infinite chain of interacting quantum (anharmonic) os- cillators. The pair potential for the oscillators at lattice distance d is proportional to (d 2 (log(d +1))F(d) -1 ) where \( {\sum _{r \in Z}}{(rF(r))^{ - 1}} 0 there exists a limiting Gibbs state which is translationally in- variant 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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