Some properties of the limiting distribution of zeros for the partition function in several complex variables

Abstract

The Yang-Lee picture of phase transitions as limit points of zeros of the partition function is considered for several complex intensive variables. The basis of the work consists of some general assumptions about the partition function and the thermodynamic limit. The main purpose is to investigate general features of the zero distribution, which, in the most important case, tends to analytic hypersurfaces. Special attention is devoted to ends, breaks (knees), and bifurcations (stars) of the limiting distribution. Also the convergence and continuity, in a certain sense, is proved for the partition function to the power one over the volume. In this work, no attention is paid to actual systems but our considerations shall be used as a starting point providing possibilities for obtaining new information about phase transitions.