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

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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.

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References

  1. Sak, J.: Recursion relations and fixed points for ferromagnets with long-range interactions. Phys. Rev. B 8, 281 (1973)

    Article  ADS  Google Scholar 

  2. Sak, J.: Low-temperature renormalization group for ferromagnets with long-range interactions. Phys. Rev. B 15, 4344 (1977)

    Article  ADS  Google Scholar 

  3. Fisher, M.E., Ma, S.K., Nickel, B.G.: Critical exponents for long-range interactions. Phys. Rev. Lett. 29, 917 (1972)

    Article  ADS  Google Scholar 

  4. Luijten, E., Blöte, H.W.J.: Boundary between long-range and short-range critical behavior in systems with algebraic interactions. Phys. Rev. Lett. 89, 025703 (2002)

    Article  ADS  Google Scholar 

  5. M. Picco, preprint arXiv:1207.1018 (2012).

  6. Blanchard, T., Picco, M., Rajabpour, M.A.: Influence of long-range interactions on the critical behavior of the Ising model. Europhys. Lett. 101, 56003 (2013)

    Article  ADS  Google Scholar 

  7. Angelini, M.C., Parisi, G., Ricci-Tersenghi, F.: Relations between short-range and long-range Ising models. Phys. Rev. E 89, 062120 (2014)

    Article  ADS  Google Scholar 

  8. Zinn-Justin, J.: Quantum Field Theory and Critical Phenomena. Oxford Univ. Press, Oxford (1996)

    MATH  Google Scholar 

  9. Ma, S.K.: Critical exponents for charged and neutral bose gases above \(\lambda \) points. Phys. Rev. Lett. 29, 1311 (1972)

  10. Abe, R., Hikami, S.: Critical exponents and scaling relations in 1/n expansion. Prog. Theor. Phys. 49, 442 (1973)

    Article  ADS  Google Scholar 

  11. Barone, L.M., Marinari, E., Organtini, G., Ricci-Tersenghi, F.: Scientific Programming. World Scientific, Singapore (2013)

    Book  MATH  Google Scholar 

Download references

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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Authors and Affiliations

  1. Laboratoire de physique théorique, École Normale Supérieure, 24 rue Lhomond, 75005, Paris, France

    E. Brezin

  2. Dipartimento di Fisica, INFN –Sezione di Roma 1, CNR – IPCF UOS Roma, Università “La Sapienza”, P.le A. Moro 5, 00185, Rome, Italy

    G. Parisi & F. Ricci-Tersenghi

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  1. E. Brezin
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  2. G. Parisi
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  3. F. Ricci-Tersenghi
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Correspondence to E. Brezin.

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Brezin, E., Parisi, G. & Ricci-Tersenghi, F. The Crossover Region Between Long-Range and Short-Range Interactions for the Critical Exponents. J Stat Phys 157, 855–868 (2014). https://doi.org/10.1007/s10955-014-1081-0

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  • DOI: https://doi.org/10.1007/s10955-014-1081-0

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