title: Universal threshold for the dynamical behavior of lattice systems with long-range interactions.
abstract: Dynamical properties of lattice systems with long-range pair interactions, decaying like 1/r(α) with the distance r, are investigated, in particular the time scales governing the relaxation to equilibrium. Upon varying the interaction range α, we find evidence for the existence of a threshold at α=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.
authors.affiliation: Instituto de Física de São Carlos, Universidade de São Paulo, 13560-970 São Carlos, São Paulo, Brazil. bachelard.romain@gmail.com
authors.forename: Romain
authors.initials: R
authors.lastname: Bachelard
authors.forename: Michael
authors.initials: M
authors.lastname: Kastner