Skip to main content
SpringerLink
Log in

Universal Long-Time Relaxation on Lattices of Classical Spins: Markovian Behavior on Non-Markovian Timescales

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

The long-time behavior of certain fast-decaying infinite temperature correlation functions on one-, two-, and three-dimensional lattices of classical spins with various kinds of nearest-neighbor interactions is studied numerically, and evidence is presented that the functional form of this behavior is either simple exponential or exponential multiplied by cosine. Due to the fast characteristic timescale of the long-time decay, such a universality cannot be explained on the basis of conventional Markovian assumptions. It is suggested that this behavior is related to the chaotic properties of the spin dynamics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. E. Balcar and S. W. Lovesey, Theory of Magnetic Neutron and Photon Scattering (Clarendon, Oxford, 1981).

    Google Scholar 

  2. A. Abragam, Principles of Nuclear Magnetism (Clarendon Press, Oxford, 1961), Chap. IV.

    Google Scholar 

  3. M. Engelsberg and I. J. Lowe, Phys. Rev. B 10:822(1974).

    Google Scholar 

  4. K. Fabricius, U. Löw, and J. Stolze, Phys. Rev. B 55:5833(1997).

    Google Scholar 

  5. B. V. Fine, cond-mat/9911230; B. V. Fine, Ph.D. thesis, University of Illinois at Urbana-Champaign (2000) (http://www.physics.uiuc.edu/Research/Publications/theses/copies/fine.ps).

  6. D. Ruelle, Phys. Rev. Lett. 56:405(1986).

    Google Scholar 

  7. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1998).

    Google Scholar 

  8. O. F. de Alcantara Bonfim and G. Reiter, Phys. Rev. Lett. 69:367(1992); M. Böhm, R. W. Gerling, and H. Leschke, Phys. Rev. Lett. 70:248(1993); O. F. de Alcantara Bonfim and G. Reiter, Phys. Rev. Lett. 70:249(1993).

    Google Scholar 

  9. N. Bloembergen, Physica 15:386(1949).

    Google Scholar 

  10. G. Müller, Phys. Rev. Lett. 60:2785(1988).

    Google Scholar 

  11. R. W. Gerling and D. P. Landau, Phys. Rev. Lett. 63:812(1989); G. Müller, Phys. Rev. Lett. 63:813(1989); R. W. Gerling and D. P. Landau, Phys. Rev. B 42:8214(1990).

    Google Scholar 

  12. In three dimensions, we have also computed correlation functions (1) for the face-centered and the body-centered cubic lattices. The nearest-neighbor interaction constants were the same as those indicated in Figs. 1(g,h). In every case, we have observed the long-time behavior (3) or (4). These results can be obtained from the author.

  13. T. Prosen, J. Phys. A 35:L737(2002).

    Google Scholar 

Download references

Author information

Author notes

  1. Boris V. Fine

    Present address: Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, D-01187, Dresden, Germany

Authors and Affiliations

  1. Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801, USA

    Boris V. Fine

  2. Spinoza Institute, Minnaert Bld., Utrecht University, Leuvenlaan 4, 3584 CE, Utrecht, The Netherlands

    Boris V. Fine

Authors
  1. Boris V. Fine
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fine, B.V. Universal Long-Time Relaxation on Lattices of Classical Spins: Markovian Behavior on Non-Markovian Timescales. Journal of Statistical Physics 112, 319–327 (2003). https://doi.org/10.1023/A:1023639906726

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1023639906726

Search

Navigation