https://doi.org/10.1140/epjb/e2020-100374-5
Regular Article
Symmetry breaking phase transitions in mean-field models triggered by double-well potentials
IFAC-CNR Institute of applied physics Nello Carrara,
Via Madonna del Piano 10,
50019
Sesto Fiorentino (FI), Italy
a e-mail: f.baroni@ifac.cnr.it; baronifab@libero.it
Received:
30
July
2019
Received in final form:
30
November
2019
Published online: 9 March 2020
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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020