2007/06/25 by Alessandro Campa, Andrea Giansanti, Gianluca Morelli
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Complex Systems and Time Series Analysis #Hamiltonian (control theory) #Hamiltonian system #Mathematics #Mean field theory #Observable #Phase transition #Physics #Quantum mechanics #Statistical Mechanics and Entropy #Statistical physics #Supercritical fluid #Thermodynamic equilibrium #Thermodynamic limit #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.76.041117
Submitted to Phys. Rev. E
arxiv created 2007/06/25 · openalex publication_date 2007/10/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Hamiltonian mean-field model has been investigated, since its introduction about a decade ago, to study the equilibrium and dynamical properties of long-range interacting systems. Here we study the long-time behavior of long-lived, out-of-equilibrium, quasistationary dynamical states, whose lifetime diverges in the thermodynamic limit. The nature of these states has been the object of a lively debate in the recent past. We introduce a numerical tool, based on the fluctuations of the phase of the instantaneous magnetization of the system. Using this tool, we study the quasistationary states that arise when the system is started from different classes of initial conditions, showing that the new observable can be exploited to compute the lifetime of these states. We also show that quasistationary states are present not only below, but also above the critical temperature of the second-order magnetic phase transition of the model. We find that at supercritical temperatures the lifetime is much larger than at subcritical temperatures.