Romain Bachelard, Michael Kastner
Dynamical properties of lattice systems with long-range pair interactions, decaying like 1/r^{\alpha} with the distance r, are investigated, in particular the timescales 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 ferro- to anti-ferromagnetic, and including a variety of lattice structures, we conjecture this threshold and some of its characteristic properties to be universal.
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http://arxiv.org/abs/1304.2922
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