Wolfram Just: Analytic properties of the Ruelle zeta-function for mean field models of phase transition
Abstract:
Zeta-functions are an important concept in different fields of theoretical physics, like equilibrium statistical mechanics, nonlinear dynamics, or semiclassical descriptions of chaotic quantum systems. Of particular interest are analytical properties of zeta­functions as they reflect nontrivial features like dynamical instabilities or phase transitions. For a simple globally coupled spin system we compute explicitly the Ruelle zeta-function. We study in detail how the ferromagnetic phase transition is reflected by changes in the analytical properties of the zeta-function.