  Resonant relaxation has been discussed as an efficient process that changes
the angular momenta of stars orbiting around a central supermassive black hole
due to the fluctuating gravitational field of the stellar cluster. Other
spherical stellar systems, such as globular clusters, exhibit a restricted form
of this effect where enhanced relaxation rate only occurs in the directions of
the angular momentum vectors, but not in their magnitudes; this is called
vector resonant relaxation (VRR). To explore this effect, we performed a large
set of direct N-body simulations, with up to 512k particles and ~500 dynamical
times. Contrasting our simulations with Spitzer-style Monte Carlo simulations,
that by design only exhibit 2-body relaxation, we show that the temporal
behavior of the angular momentum vectors in $N$-body simulations cannot be
explained by 2-body relaxation alone. VRR operates efficiently in globular
clusters with $N>10^4$. The fact that VRR operates in globular clusters may
open way to use powerful tools in statistical physics for their description. In
particular, since the distribution of orbital planes relaxes much more rapidly
than the distribution of the magnitude of angular momentum and the radial
action, the relaxation process reaches an internal statistical equilibrium in
the corresponding part of phase space while the whole cluster is generally out
of equilibrium, in a state of quenched disorder. We point out the need to
include effects of VRR in Monte Carlo simulations of globular clusters.
