Existence of Quasi-stationary states at the Long Range threshold

TL;DR

This paper investigates the lifetime of quasi-stationary states in the $ ext{α-HMF}$ model at the long-range threshold ($ ext{α=1}$), revealing a logarithmic divergence with system size and identifying a phase transition at $ ext{α=1.5}$.

Contribution

It demonstrates the existence and scaling behavior of QSS at the long-range threshold and discusses the nature of long-range interactions beyond this point.

Findings

QSS exist at $ ext{α=1}$ with lifetime $ au(N) o ext{log} N$

A phase transition occurs at $ ext{α=1.5}$

Long-range interactions are characterized and discussed

Abstract

In this paper the lifetime of quasi-stationary states (QSS) in the $\alpha-$HMF model are investigated at the long range threshold ($\alpha=1$). It is found that QSS exist and have a diverging lifetime $\tau(N)$ with system size which scales as $\mbox{\ensuremath{\tau}(N)\ensuremath{\sim}}\log N$, which contrast to the exhibited power law for $\alpha<1$ and the observed finite lifetime for $\alpha>1$. Another feature of the long range nature of the system beyond the threshold ($\alpha>1$) namely a phase transition is displayed for $\alpha=1.5$. The definition of a long range system is as well discussed.