THERMAL EFFECT IN LIPKIN MODEL .2. GRAND PARTITION-FUNCTION AND MEAN-FIELD APPROXIMATION

In a previous paper, referred to as I, we developed a new approach for the description of thermal effects in the Lipkin model. In order to c larify the physical ingredient of this approach, we introduce the gran d partition function of the present system. We compare numerically the results from these two approaches and show that they nearly coincide, except for the region near the transition temperature. Further, we sh ow that our approach is equivalent to that based on the grand partitio n function under the mean field approximation.