We numerically study, from first principles, the temperature $T_{\mathrm{QSS}}$ and duration $t_{\mathrm{QSS}}$ of the longstanding initial quasi-stationary state of the isolated $d$-dimensional classical inertial $\alpha \text{−}XY$ ferromagnet with two-body interactions decaying as $1/r_{ij}^{\alpha }$ $(\alpha \ge 0)$. It is shown that this temperature $T_{\mathrm{QSS}}$ (defined proportional to the kinetic energy per particle) depends, for the long-range regime $0\le \alpha /d\le 1$, on $(\alpha ,d,U,N)$ 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 $T_{\mathrm{QSS}}-T_{\infty }\propto 1/N^{\beta }$ where $T_{\infty }\equiv 2U-1$ for $U\lesssim U_c$, and $\beta$ appears to depend sensibly only on $\alpha /d$. Our numerical results indicate that neither the scaling with $N$ of $T_{\mathrm{QSS}}$ nor that of $t_{\mathrm{QSS}}$ depend on $U$.

A. Rodríguez, F. Nobre, C. Tsallis, Finite-size scaling of quasi-stationary-state temperature, Physical Review E 105(4) (2022) 044111.