Abstract

Polyacetylene (CH) χ, a one-dimensional polymer, is studied as a model of quantum statistical mechanics. The effective Gibbs measure of phonons in (CH) χ is obtained by integrating out the fermion degrees of freedom, and it is shown that the effective interactions of phonons are rather complicated many-body ones but of short range (at least for small coupling constant g or for small inverse temperature β). Thus the Araki-Ruelle theory implies non-existence of long-range orders in this system.

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