On the XY-model on two-sided infinite chain (Q796798)

The XY-model on the one-dimensional lattice, infinitely extended to both directions, is studied by a method of \(C^*\)-algebra. The following three features are found different from the same model on one-sided infinite chain studied by \textit{H. Araki} and \textit{E. Barouch} [J. Stat. Phys. 31, 327-345 (1983)]: (1) There are no non-trivial constant observables. (2) The (twisted) asymptotic abelian property holds only partially and not for general observable operators. (3) Return to equilibrium occurs for all values of the parameter \(\gamma\) and is proved by a method different from the case of one-sided chain.