Clustering and ensembles inequivalence in the φ and φ mean-field Hamiltonian models

We investigate a model of globally coupled conservative oscillators. Two different algebraic potentials are considered that display in the canonical ensemble either a second (φ⁴) or both a second and a first-order phase transition separated by tricritical points (φ⁶). The stability of highly clustered states appearing in the low temperature/energy region is studied both analytically and numerically for the φ⁴-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 φ⁶-model show strong hysteretic effects and metastability near the first-order phase transition and a narrow region of negative specific heat.