  Universality is a crucial concept in modern physics, allowing us to capture
the essential features of a system's behavior using a small set of parameters.
In this work, we unveil universal spin relaxation dynamics in anisotropic
random Heisenberg models with infinite-range interactions at high temperatures.
Starting from a polarized state, the total magnetization can relax
monotonically or decay with long-lived oscillations, determined by the sign of
a universal single function $A=-\xi_1^2+\xi_2^2-4\xi_2\xi_3+\xi_3^2$. Here
$(\xi_1,\xi_3,\xi_3)$ characterizes the anisotropy of the Heisenberg
interaction. Furthermore, the oscillation shows up only for $A>0$, with
frequency $\Omega \propto \sqrt{A}$. To validate our theory, we compare it to
numerical simulations by solving the Kadanoff-Baym (KB) equation with a melon
diagram approximation and the exact diagonalization (ED). The results show our
theoretical prediction works in both cases, regardless of a small system size
$N=8$ in ED simulations. Our study sheds light on the universal aspect of
quantum many-body dynamics beyond low energy limit.
