Criticality in the duration of quasistationary state

Details

The duration of the quasistationary states (QSSs) emerging in the $d$-dimensional classical inertial $\alpha \text{−}XY$ model, i.e., $N$ planar rotators whose interactions decay with the distance $r_{ij}$ as $1/r_{ij}^{\alpha }$ ($\alpha \ge 0$), is studied through first-principles molecular dynamics. These QSSs appear along the whole long-range interaction regime ($0\le \alpha /d\le 1$), for an average energy per rotator $U<U_c$ ($U_c=3/4$), and they do not exist for $U>U_c$. They are characterized by a kinetic temperature $T_{\text{QSS}}$, before a crossover to a second plateau occurring at the Boltzmann-Gibbs temperature $T_{\text{BG}}>T_{\text{QSS}}$.

We investigate here the behavior of their duration $t_{\text{QSS}}$ when $U$ approaches $U_c$ from below, for large values of $N$. Contrary to the usual belief that the QSS merely disappears as $U\to U_c$, we show that its duration goes through a critical phenomenon, namely $t_{\text{QSS}}\propto {({}_c-U)}^{-\xi }$. Universality is found for the critical exponent $\xi \simeq 5/3$ throughout the whole long-range interaction regime.

A. Rodríguez, F. Nobre, C. Tsallis, Criticality in the duration of quasistationary state, Physical Review E 104 (2021) 014144