A simple topological model with continuous phase transition

Details A simple topological model with continuous phase transition A simple topological model with continuous phase transition

2011-02-16

arxiv.org/abs/1102.3276v5

Physics

Condensed Matter

Statistical Mechanics

17 pages, 7 figures

Scientific paper

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.

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