Finite-size scaling of quasi-stationary-state temperature

We numerically study, from first principles, the temperature T_{QSS} and duration t_{QSS} of the longstanding initial quasi-stationary state of the isolated d-dimensional classical inertial α-XY ferromagnet with two-body interactions decaying as 1/r_{ij}^{α} (α≥0). It is shown that this temperature T_{QSS} (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 T_{QSS}-T_{∞}∝1/N^{β} where T_{∞}≡2U-1 for U≲U_{c}, and β appears to depend sensibly only on α/d. Our numerical results indicate that neither the scaling with N of T_{QSS} nor that of t_{QSS} depend on U.