Rodriguez, Antonio; Fernando D. Nobre and Constantino Tsallis

The duration of the quasistationary states (QSSs) emerging in the d-dimensional classical inertial α−XY model, i.e., N planar rotators whose interactions decay with the distance r ij as 1/r α ij (α ≥ 0), is studied through first-principles molecular dynamics. These QSSs appear along the whole long-range interaction regime (0 ≤ α/d ≤ 1), 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 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 Uc from below, for large values of N. Contrary to the usual belief that the QSS merely disappears as U →Uc, we show that its duration goes through a critical phenomenon, namely t QSS ∝ (Uc − U) −ξ. Universality is found for the critical exponent ξ ≃ 5/3 throughout the whole long-range interaction regime.