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

TL;DR

This paper investigates how the relaxation times of lattice systems with long-range interactions depend on the interaction decay rate, identifying a universal threshold at /2 that marks a change in dynamical behavior.

Contribution

It proposes a universal threshold at /2 for the dynamical behavior change in long-range lattice systems, supported by analytical and numerical evidence across diverse models.

Findings

Existence of a threshold at /2 for relaxation behavior

Change in scaling exponents at the threshold

Universality of the threshold across different systems

Abstract

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.