Metastable states, anomalous distributions and correlations in the HMF model

TL;DR

This paper investigates the microscopic dynamics of metastable states in the Hamiltonian Mean Field model, revealing non-Gaussian distributions, anomalous correlations, and the relevance of Tsallis nonextensive statistics in out-of-equilibrium phases.

Contribution

It provides a detailed analysis of how different initial conditions affect metastability, correlations, and relaxation dynamics in the HMF model, highlighting the role of Tsallis statistics.

Findings

Non-Gaussian velocity PDFs in QSS

Anomalous correlations present only with initial magnetization one

Power-law decay and aging phenomena observed in certain conditions

Abstract

We study the microscopic dynamics of the metastable Quasi-Stationary States (QSS) in the Hamiltonian Mean Field (HMF) model, a Hamiltonian system of N classical inertial spins with infinite-range interactions which shows a second order phase transition. In order to understand the origin of metastability, which appears in an energy region below the critical point, we consider two different classes of out-of-equilibrium initial conditions, both leading to QSS, and having respectively initial magnetization equal to one (M1 IC) and equal to zero (M0 IC). We compare the corresponding $\mu$-space, the resulting velocity pdfs and correlations, and the eventual aging features of the microscopic dynamics. In both cases the model exhibits non-gaussian pdfs, though anomalous correlations are present only when the system is started with an initial magnetization equal to one. In the M0 IC case the relaxation to equilibrium is almost exponential, while,for M1 IC, when correlations and aging are found, the decay is a power-law and the overall behavior can be very well reproduced by a Tsallis q-exponential function. These results contribute to clarify the overall scenario, which is more complex than previously expected and stress the importance of the dynamics in the relaxation process. The nonextensive statistical mechanics formalism proposed by Tsallis seems to be valid, in the out-of-equilibrium phase, when correlations and strong long-term memory effects emerge. This regime becomes stable if the $N\to \infty $ limit is performed before the $t\to \infty $ limit.