A simple topological model with continuous phase transition

In the area of topological and geometric treatment of phase transitions and symmetry breaking in Hamiltonian systems, some general sufficient conditions for these phenomena in Z(2)-symmetric systems (i.e. invariant under reflection of coordinates) were found in a recent paper. In this paper we present a simple topological model satisfying the above conditions, hoping to shed light on the mechanism which causes this phenomenon in more general physical models. The symmetry breaking is proved by a continuous magnetization with a nonanalytic point in correspondence with a critical temperature which divides the broken symmetry phase from the unbroken one. A particularity with respect to the common pictures of a phase transition is that the nonanalyticity of the magnetization is not accompanied by a nonanalytic behavior of the free energy.