  Dynamical properties of lattice systems with long-range pair interactions,
decaying like 1/r^{\alpha} with the distance r, are investigated, in particular
the time scales governing the relaxation to equilibrium. Upon varying the
interaction range \alpha, we find evidence for the existence of a threshold at
\alpha=d/2, dependent on the spatial dimension d, at which the relaxation
behavior changes qualitatively and the corresponding scaling exponents switch
to a different regime. Based on analytical as well as numerical observations in
systems of vastly differing nature, ranging from quantum to classical, from
ferromagnetic to antiferromagnetic, and including a variety of lattice
structures, we conjecture this threshold and some of its characteristic
properties to be universal.
