Scale invariant forces in 1d shuffled lattices

Details Scale invariant forces in 1d shuffled lattices Scale invariant forces in 1d shuffled lattices

2005-06-15

arxiv.org/abs/cond-mat/0506365v2

Phys. Rev. E, 72, 066113 (2005)

Physics

Condensed Matter

Statistical Mechanics

10 pages, revtex4 format

Scientific paper

10.1103/PhysRevE.72.066113

In this paper we present a detailed and exact study of the probability density function $P(F)$ of the total force $F$ acting on a point particle belonging to a perturbed lattice of identical point sources of a power law pair interaction. The main results concern the large $F$ tail of $P(F)$ for which two cases are mainly distinguished: (i) Gaussian-like fast decreasing $P(F)$ for lattice with perturbations forbidding any pair of particles to be found arbitrarily close to one each other; (ii) L\'evy-like power law decreasing $P(F)$ when this possibility is instead permitted. It is important to note that in the second case the exponent of the power law tail of $P(F)$ is the same for all perturbation (apart from very singular cases), and is in an one to one correspondence with the exponent characterizing the behavior of the pair interaction with the distance between the two particles.

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