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

Thierry Dauxois·Stefano Lepri·Stefano Ruffo
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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 ($ϕ^{4}$) or both a second and a first order phase transition separated by tricritical points ($ϕ^{6}$). The stability of highly clustered states appearing in the low temperature/energy region is studied both analytically and numerically for the $ϕ^{4}$-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 $ϕ^{6}$-model show strong hysteretic effects and metastability near the first-order phase transition and a narrow region of negative specific heat.

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Thierry Dauxois, Stefano Lepri, Stefano Ruffo. 2003-04-08. Clustering and ensembles inequivalence in the phi-4 and phi-6 mean-field Hamiltonian models. https://doi.org/10.1016/s1007-5704(03)00055-8

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