Models with symmetry-breaking phase transitions triggered by dumbbell-shaped equipotential surfaces.,Physical Review E

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Models with symmetry-breaking phase transitions triggered by dumbbell-shaped equipotential surfaces.
Physical Review E ( IF 2.2 ) Pub Date : 2020-07-08 , DOI: 10.1103/physreve.102.012119
Fabrizio Baroni ₁

Affiliation

Recently, a number of sufficiency conditions have been shown for the occurrence of a

Z_{2}

-symmetry breaking phase transition (

Z_{2}

-SBPT) starting from geometric-topological concepts of potential energy landscapes. In particular, a

Z_{2}

-SBPT can be triggered by double-well potentials, or equivalently by dumbbell-shaped equipotential surfaces. In this paper, we introduce two models with a

Z_{2}

-SBPT that, due to their essential feature, show in the clearest way the generating mechanism of a

Z_{2}

-SBPT. Although they cannot be considered physical models, they all have the features of such models with the same kind of SBPT. At the end of the paper, the

ϕ^{4}

model is revisited in light of this approach. In particular, the landscape of one of the models introduced here turned out to be equivalent to that of the mean-field