Models with symmetry-breaking phase transitions triggered by dumbbell-shaped equipotential surfaces

Fabrizio Baroni
Phys. Rev. E 102, 012119 – Published 8 July 2020

Abstract

Recently, a number of sufficiency conditions have been shown for the occurrence of a Z2-symmetry breaking phase transition (Z2-SBPT) starting from geometric-topological concepts of potential energy landscapes. In particular, a Z2-SBPT can be triggered by double-well potentials, or equivalently by dumbbell-shaped equipotential surfaces. In this paper, we introduce two models with a Z2-SBPT that, due to their essential feature, show in the clearest way the generating mechanism of a Z2-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 ϕ4 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 ϕ4 model in a simplified version.

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  • Received 27 February 2020
  • Revised 11 June 2020
  • Accepted 17 June 2020

DOI:https://doi.org/10.1103/PhysRevE.102.012119

©2020 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Statistical Physics & Thermodynamics

Authors & Affiliations

Fabrizio Baroni*

  • IFAC-CNR Institute of Applied Physics “Nello Carrara,” Via Madonna del Piano 10, I-50019 Sesto Fiorentino (FI), Italy

  • *f.baroni@ifac.cnr.it, baronifab@libero.it

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Vol. 102, Iss. 1 — July 2020

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