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Symmetry breaking phase transitions in mean-field models triggered by double-well potentials

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Abstract

We present a general rule to shape a long-range potential of a Hamiltonian system for a ℤ2-symmetry breaking phase transition (ℤ2-SBPT) to occur. The main feature is a double-well potential which competes with the entropy in shaping the free energy accordingly to Landau mean-field theory of SBPTs. Further, we introduce a classical spin model undergoing a first-order ℤ2-SBPT which was born from the effort to find one of the simplest way to generate such a phenomenon by means of a double-well potential. The model may be suitable also for didactic purposes and for numerical investigation of the dynamic near the transition point. Finally, we revisit the Ising model and the spherical model (Berlin-Kac) in mean-field version showing the double-well potential at work.

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Authors and Affiliations

  1. IFAC-CNR Institute of applied physics Nello Carrara, Via Madonna del Piano 10, 50019, Sesto Fiorentino (FI), Italy

    Fabrizio Baroni

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  1. Fabrizio Baroni
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Correspondence to Fabrizio Baroni.

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Baroni, F. Symmetry breaking phase transitions in mean-field models triggered by double-well potentials. Eur. Phys. J. B 93, 45 (2020). https://doi.org/10.1140/epjb/e2020-100374-5

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  • DOI: https://doi.org/10.1140/epjb/e2020-100374-5

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