Thermal effect in Lipkin model. 1. Thermal equilibrium state and phase transition

We study the thermal effect with the use of Lipkin model. We define the density and entropy operator associated with the mixed state representation of Lipkin model, which has been developed with the aid of auxiliary fermion field. We investigate the thermal equilibrium state and its phase transition. In super phase, the thermal effect breaks the particle-hole pairs with coupled angular momentum 0 and does not lift up nucleons from the lower level to upper one, contrary to the case of normal phase. (author)