Determinant Representation for time and temperature dependent correlation functions in the isotropic XY model in the transverse magnetic field

Abstract

Astymptotics of temperature correlations is the most dificult problem of stat. mech. Recently it was solved for the impenetrable Bose Gas. The idea is to represent correlation function as $τ$ function of calssical completely integrable differential equation. Now we start to apply this program to isotropic XY model in the trasnsverse magnetic field. In this paper we are making first step. We representing correlation function as detrminanat of an integral operator.