Existence of quasi-stationary states at the long range threshold

Abstract

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.