Skip to main content
Log in

Microcanonical Finite-Size Scaling

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

Abstract

In the microcanonical ensemble, suitably defined observables show nonanalyticities and power-law behavior even for finite systems. For these observables, a microcanonical finite-size scaling theory is established and combined with the experimentally observed power-law behavior. Scaling laws are obtained which relate exponents of the finite system and critical exponents of the infinite system to the system-size dependence of the affiliated microcanonical observables.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. D. Ruelle, Statistical Mechanics: Rigorous Results (W. A. Benjamin, Reading, 1969).

    Google Scholar 

  2. M. E. Fischer and M. N. Barber, Scaling theory for finite-size effects in the critical region, Phys. Rev. Lett. 28:1516 (1972).

    Google Scholar 

  3. R. C. Desai, D. W. Heermann, and K. Binder, Finite-size scaling in a microcanonical ensemble, J. Stat. Phys. 53:795 (1988).

    Google Scholar 

  4. M. Kastner, M. Promberger, and A. Hüller, in Computer Simulation Studies in Condensed Matter Physics XI, D. P. Landau and H.-B. Schüttler, eds. (Heidelberg, 1998).

  5. The zero-field magnetization and the susceptibility can be expressed in terms of ɛ, ɛ* or \(\tilde \varepsilon \). The corresponding functions are denoted by m, χ m*, χ* or \(\tilde m\), \(\tilde \chi \).

  6. M. Kastner, Critical phenomena in the entropy formalism and microcanonical finite-size scaling, Ph.D. thesis (Erlangen, 2000).

  7. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford, 1971).

  8. M. N. Barber, in Phase Transitions and Critical Phenomena, Vol. 8, C. Domb and M. S. Green, eds. (Academic Press, London, 1983).

    Google Scholar 

  9. C. DiCastro, G. Jona-Lasinio, in Phase Transitions and Critical Phenomena, Vol. 6, C. Domb and M. S. Green, eds. (London, 1976).

  10. M. Promberger, On a trivial aspect of canonical specific heat scaling, cond-mat/9904297.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kastner, M., Promberger, M. & Hüller, A. Microcanonical Finite-Size Scaling. Journal of Statistical Physics 99, 1251–1264 (2000). https://doi.org/10.1023/A:1018636705716

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018636705716

Navigation