Gibbs states of a one dimensional quantum lattice

A one dimensional infinite quantum spin lattice with a finite range interaction is studied. The Gibbs state in the infinite volume limit is shown to exist as a primary state of a UHF algebra. The expectation value of any local observables in the state as well as the mean free energy depend analytically on the potential, showing no phase transition. The Gibbs state is an extremal KMS state.On leave from Research Institute for Mathematical Sciences, Kyoto University Kyoto, Japan.