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

TL;DR

This paper explores phase transitions, clustering, and metastability in mean-field Hamiltonian models with phi-4 and phi-6 potentials, revealing ensemble inequivalence and out-of-equilibrium phenomena through analytical and numerical methods.

Contribution

It provides a comparative analysis of phase transition behaviors and stability of clustered states in phi-4 and phi-6 mean-field models, highlighting ensemble inequivalence and metastability.

Findings

Highly clustered states are stable at low energies.

Long-lived out-of-equilibrium states occur near second-order transitions.

Hysteresis and negative specific heat are observed near first-order transitions.

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