A model with symmetry-breaking phase transition triggered by a double-well potential

2020/06/23 by Fabrizio Baroni, Baroni, F.
Earth and Planetary Sciences · Physics and Astronomy · #FOS: Physical sciences #Force Microscopy Techniques and Applications #High-pressure geophysics and materials #Quantum, superfluid, helium dynamics #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.2006.13734

openalex publication_date 2020/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In some recent papers some theorems on sufficiency conditions for the occurrence of a ℤ₂-symmetry breaking phase transition (ℤ₂-SBPT) have been showed making use of geometric-topological concepts of potential energy landscapes. In particular, a ℤ₂-SBPT can be triggered by double-well potentials, or in an equivalent way, by dumbbell-shaped equipotential surfaces. In this paper we introduce a model with a classical ℤ₂-SBPT which, due to its essential feature, shows in the clearest way the generating-mechanism of a ℤ₂-SBPT above mentioned. Despite the model is not a physical model, it has all the features of such a model with the same kind of SBPT. At the end of the paper a comparison with the ϕ⁴ model is made. The model may be useful for didactic purposes.

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