Transfer operators and dynamical zeta functions for a class of lattice spin models

Abstract

We investigate the location of zeros and poles of a dynamical zeta function arizing in a class of lattice spin models introduced in the 60-ties by M. Kac. The transfer operator method allows us to prove the xistence of infinitely nontrivial zeros of this function on the real line. For certain parameter values there exist also infinitely many trivial equally spaced zeros on a line parallel to the imaginary axis. Hence also for this kind of dynamical zeta function some kind of Riemann hypothesis seems to hold.