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An \(\mathsf{\epsilon}\)-expansion for small-world networks

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Abstract.

I construct a well-defined expansion in \(\epsilon = 2-d\) for diffusion processes on small-world networks. The technique permits one to calculate the average over disorder of moments of the Green’s function, and is used to calculate the average Green’s function and fluctuations to first non-leading order in \(\epsilon\), giving results which agree with numerics. This technique is also applicable to other problems of diffusion in random media.

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References

  1. D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998)

    Article  Google Scholar 

  2. R. Albert, A.-L. Barabasi, Rev. Mod. Phys. 74, 47 (2002)

    Article  MathSciNet  Google Scholar 

  3. R. Monasson, Eur. Phys. J. B. 12, 555 (1999)

    Google Scholar 

  4. B. Kozma, M.B. Hastings, G. Korniss, Phys. Rev. Lett. 92, 108701 (2004)

    Google Scholar 

  5. M.B. Hastings, Phys. Rev. Lett. 91, 098701 (2003)

    Google Scholar 

  6. J. Rammer, Rev. Mod. Phys. 63, 781 (1991)

    Google Scholar 

  7. A.B. Harris, J. Phys. C 7, 1671 (1974)

    Article  Google Scholar 

  8. A.W.W. Ludwig, Nucl. Phys. B 285, 97 (1987)

    Google Scholar 

  9. M. Bramson, J.L. Lebowitz, Phys. Rev. Lett. 61, 2397 (1998)

    Google Scholar 

  10. A.A. Ovchinikov, Ya.B. Zeldovich, Chem. Phys. 28, 214 (1978)

    Google Scholar 

Download references

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Authors and Affiliations

  1. T-13 and Center for Nonlinear Studies, Los Alamos National Laboratory, NM 87545, Los Alamos, USA

    M. B. Hastings

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  1. M. B. Hastings
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Correspondence to M. B. Hastings.

Additional information

Received: 28 July 2004, Published online: 14 December 2004

PACS:

89.75.Hc Networks and genealogical trees 64.60.Ak Renormalization-group studies of phase transitions

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Hastings, M.B. An \(\mathsf{\epsilon}\)-expansion for small-world networks. Eur. Phys. J. B 42, 297–301 (2004). https://doi.org/10.1140/epjb/e2004-00383-6

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  • DOI: https://doi.org/10.1140/epjb/e2004-00383-6

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