English

The crossover region between long-range and short-range interactions for the critical exponents

Statistical Mechanics 2014-12-30 v1

Abstract

It is well know that systems with an interaction decaying as a power of the distance may have critical exponents that are different from those of short-range systems. The boundary between long-range and short-range is known, however the behavior in the crossover region is not well understood. In this paper we propose a general form for the crossover function and we compute it in a particular limit. We compare our predictions with the results of numerical simulations for two-dimensional long-range percolation.

Keywords

Cite

@article{arxiv.1407.3358,
  title  = {The crossover region between long-range and short-range interactions for the critical exponents},
  author = {Edouard Brezin and Giorgio Parisi and Federico Ricci-Tersenghi},
  journal= {arXiv preprint arXiv:1407.3358},
  year   = {2014}
}

Comments

17 pages, 6 figures

R2 v1 2026-06-22T05:02:35.053Z