Clustering and ensembles inequivalence in the / 4 and / 6 mean-field Hamiltonian models

Thierry Dauxois (1) , Stefano Lepri (1, 2) , Stefano Ruffo (1, 2)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
2 Dipartimento di Fisica e Astronomia [Firenze]

We investigate a model of globally coupled conservative oscillators. Two different algebraic potentials are considered that display in the canonical ensemble either a second (/ 4) or both a second and a first-order phase transition separated by tricritical points (/ 6). The stability of highly clustered states appearing in the low temperature/energy region is studied both analytically and numerically for the / 4-model. Moreover, long-lived out-of-equilibrium states appear close to the second-order phase transition when starting with ''water-bag'' initial conditions, in analogy with what has been found for the Hamiltonian mean-field model. The microcanonical simulations of the / 6-model show strong hysteretic effects and metastability near the first-order phase transition and a narrow region of negative specific heat.

Mots clés: Long-range interaction; Coherent structures; Mean-field; Microcanonical ensemble

Domaines: Mécanique statistique [cond-mat.stat-mech]

Thierry Dauxois, Stefano Lepri, Stefano Ruffo. Clustering and ensembles inequivalence in the / 4 and / 6 mean-field Hamiltonian models. Communications in Nonlinear Science and Numerical Simulation, 2003, pp.375-387. ⟨10.1016/S1007-5704(03)00055-8⟩. ⟨hal-01140182⟩