Instability of thermal equilibrium state of the Lipkin model

The Lipkin model is the simplest algebraic model in which we can investigate a ground state transition in a fermion system. This model is also applied to the description of the thermal equilibrium state. In this paper, we investigate its stability with respect to changes in the particle number and the volume. In order to enable us to take the thermal limit, an appropriate number dependence is introduced into the force strength. We show with the use of a mean field approximation that the thermal equilibrium state in the condensed phase of particle-hole pairs becomes unstable. (author)