A simple topological model with continuous phase transition

TL;DR

This paper introduces a simple topological model demonstrating a continuous phase transition with symmetry breaking, where magnetization exhibits nonanalytic behavior without affecting the free energy, providing insights into phase transition mechanisms.

Contribution

It presents a minimal topological model satisfying recent conditions for symmetry breaking, highlighting a unique phase transition where magnetization is nonanalytic but free energy remains analytic.

Findings

Magnetization shows a nonanalytic point at critical temperature.

The phase transition occurs without nonanalyticity in free energy.

The model supports topological explanations of symmetry breaking.

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.