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Journal of Statistical Physics

, Volume 157, Issue 4–5, pp 855–868 | Cite as

The Crossover Region Between Long-Range and Short-Range Interactions for the Critical Exponents

  • E. BrezinEmail author
  • G. Parisi
  • F. Ricci-Tersenghi
Article

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

Critical phenomena Percolation with long-range interactions  Cross-over to shortrange 

Notes

Acknowledgments

This research has received financial support from the European Research Council (ERC) through grant agreement No. 247328 and from the Italian Research Minister through the FIRB Project No. RBFR086NN1.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Laboratoire de physique théoriqueÉcole Normale SupérieureParisFrance
  2. 2.Dipartimento di FisicaINFN –Sezione di Roma 1, CNR – IPCF UOS Roma, Università “La Sapienza”RomeItaly

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