Existence of Quasi-stationary states at the Long Range threshold

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

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