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

Abstract

We investigate a model of globally coupled conservative oscillators. Two different algebraic potentials are considered that display in the canonical ensemble either a second (${\varphi }^4$) or both a second and a first order phase transition separated by tricritical points (${\varphi }^6$). The stability of highly clustered states appearing in the low temperature/energy region is studied both analytically and numerically for the ${\varphi }^4$-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 (HMF) model. The microcanonical simulations of the ${\varphi }^6$-model show strong hysteretic effects and metastability near the first-order phase transition and a narrow region of negative specific heat.

To appear in the proceedings of the workshop "Chaotic Transport and Complexity in classical and quantum dynamics", Communications in Nonlinear Science and Numerical Simulation (2003)