Quasi-stationary-state duration in d-dimensional long-range model

Through first-principles molecular dynamics we study a d-dimensional classical inertial Heisenberg model with a range interaction decaying with distance r as 1/rα (α ? 0); α = 0 (α → ∞) corresponds to infinite- ij ij range (nearest-neighbor) interactions; the ratio α/d > 1 (0 ? α/d ? 1) characterizes the short-range (long- range) interactions regime. In the long-range regime, a quasi-stationary state (QSS), characterized by a temperature TQSS, emerges before a crossover to a second plateau, corresponding to the Boltzmann-Gibbs (BG) temperature TBG (as predicted within the BG theory). The QSS duration tQSS depends on the system size N, α, and d: the dependence on α appears only through the ratio α/d, and tQSS decreases (increases) with α/d (with N and d). It has been possible, for fixed energy per particle, to analytically scale all these dependencies through a universal form; namely, tQSS ∝ NA(α/d)e−B(N)(α/d)2 . This paves the way for other long-range Hamiltonian systems, such as gravitation, the α-XY , and Coulombian models, among others.