Universal threshold for the dynamical behavior of lattice systems with long-range interactions

Romain Bachelard, Michael Kastner

Published 2013-04-10, updated 2013-04-29Version 2

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.