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 equals to one). It is found that QSS exist and have a diverging lifetime with system size which scales logaritmically with the number of constituents. This contrast to the exhibited power law below the long range threshold (α smaller than one) and the observed finite lifetime beyond. Also even beyond this long range threshold the long range nature of the system is displayed, namely the existence of a phase transition. As a consequence of our findings the definition of a long range system is discussed.

► Existence of quasi-stationary states at the long range threshold.
► Observation of a phase transition above the threshold.
► Derivation of a fractional equation governing the dynamics.