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.

• Received 21 November 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.170603