Rodriguez, Antonio; Fernando D. Nobre and Constantino Tsallis

We numerically study, from first principles, the temperature TQSS and duration tQSS of the longstanding initial quasi-stationary state of the isolated d -dimensional classical inertial α−XY ferromagnet with two-body interactions decaying as 1/rαij (α ≥ 0). It is shown that this temperature TQSS (defined proportional to the kinetic energy per particle) depends, for the long-range regime 0 ≤ α/d ≤ 1, on (α, d, U, N) with numerically negligible changes for dimensions d = 1, 2, 3, with U the energy per particle and N the number of particles. We verify the finite-size scaling TQSS − T∞ ∝1/Nβ where T∞ ≡ 2U − 1 for U ≲ Uc, and β appears to depend sensibly only on α/d. Our numerical results indicate that neither the scaling with N of TQSS nor that of tQSS depend on U.