Periodic Gibbs states

Periodic Gibbs states for quantum lattice systems are investigated. We formulate the definition of the periodic Gibbs states and the measures associated with them. Theorems of existence are proved for these states. We also prove the existence of the critical temperature for the system of anharmonic quantum oscillators with pairwise interaction.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 451–458, April, 1993.