Criticality in the duration of the quasistationary state of the d-dimensional α-Heisenberg ferromagnet

The duration of the quasistationary states (QSSs) emerging in the d-dimensional classical inertial alpha Heisenberg model, i.e., N three-dimensional rotators whose interactions decay with distance r(ij) as 1/r(ij)(alpha) (alpha >= 0), is studied through first-principle molecular dynamics. These QSSs appear for the very-long-range interaction regime (0 <= alpha/d <= 1), for an average energy per rotator U < U-c (U-c = 5/6), and they do not exist for U > U-c. They are characterized by a kinetic temperature T-QSS, before a crossover to a second plateau occurring at the Boltzmann-Gibbs temperature T-BG > T-QSS. We investigate here the behavior of their duration t(QSS) when U approaches U(c )from below, for large values of N. The QSS gradually disappears as U -> U-c, while its duration undergoes a critical phenomenon, namely t(QSS) alpha (U-c - U )(-xi). Universality is found for the critical exponent xi = 1.67 +/- 0.02 throughout the very-long-range interaction regime.