Phase space gaps and ergodicity breaking in systems with long range interactions

Freddy Bouchet (1, 2) , Thierry Dauxois (2) , David Mukamel (2, 3) , Stefano Ruffo (2, 4)

1 INLN - Institut Non Linéaire de Nice Sophia-Antipolis
2 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
3 Weizmann Institute
4 Dipartimento di Energetica

We study a generalized isotropic XY-model which includes both two-spin and four-spin mean-field interactions. This model can be solved in the microcanonical ensemble. It is shown that in certain parameter regions the model exhibits gaps in the magnetization at fixed energy, resulting in ergodicity breaking. This phenomenon has previously been reported in anisotropic and discrete spin models. The entropy of the model is calculated and the microcanonical phase diagram is derived, showing the existence of first order phase transitions from the ferromagnetic to a paramagnetic disordered phase. It is found that ergodicity breaking takes place both in the ferromagnetic and the paramagnetic phases. As a consequence, the system can exhibit a stable ferromagnetic phase within the paramagnetic region, and conversely a disordered phase within the magnetically ordered region.

Keywords: Ergodicity breaking; Long-range interaction

Domains: Physics [physics]; Condensed Matter [cond-mat]; Statistical Mechanics [cond-mat.stat-mech]; Physics [physics]; Physics [physics]; General Physics [physics.gen-ph]

Freddy Bouchet, Thierry Dauxois, David Mukamel, Stefano Ruffo. Phase space gaps and ergodicity breaking in systems with long range interactions. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2008, 77, pp.011125. ⟨10.1103/PhysRevE.77.011125⟩. ⟨ensl-00184817⟩