Criticality in the duration of quasistationary state


The duration of the quasistationary states (QSSs) emerging in the d-dimensional classical inertial αXY model, i.e., N planar rotators whose interactions decay with the distance rij as 1/rαij (α0), is studied through first-principles molecular dynamics. These QSSs appear along the whole long-range interaction regime (0α/d1), for an average energy per rotator U<Uc (Uc=3/4), and they do not exist for U>Uc. They are characterized by a kinetic temperature TQSS, before a crossover to a second plateau occurring at the Boltzmann-Gibbs temperature TBG>TQSS.

We investigate here the behavior of their duration tQSS when U approaches Uc from below, for large values of N. Contrary to the usual belief that the QSS merely disappears as UUc, we show that its duration goes through a critical phenomenon, namely tQSS(UcU)ξ. Universality is found for the critical exponent ξ5/3 throughout the whole long-range interaction regime.

A. Rodríguez, F. Nobre, C. Tsallis, Criticality in the duration of quasistationary state, Physical Review E 104 (2021) 014144