A simple topological model with continuous phase transition

Abstract

In the area of topological and geometric treatment of phase transitions and symmetry breaking in Hamiltonian systems, in a recent paper some general sufficient conditions for these phenomena in ${\mathbb{Z}}_2$-symmetric systems (i.e. invariant under reflection of coordinates) have been found out. In this paper we present a simple topological model satisfying the above conditions hoping to enlighten the mechanism which causes this phenomenon in more general physical models. The symmetry breaking is testified by a continuous magnetization with a nonanalytic point in correspondence of 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.

17 pages, 7 figures

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Cited by in corpus (5)

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• Models with symmetry-breaking phase transitions triggered by dumbbell-shaped equipotential surfaces
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• Simplified energy landscape of the ${\varphi }^4$ model and the phase transition