Skip to main content
SpringerLink
Log in

Simple solution of two-dimensional ising model on a torus in terms of Grassmann integrals

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

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

Literature Cited

  1. L. Onsager, Phys. Rev.,65, 117 (1944).

    Google Scholar 

  2. B. Kaufman, Phys. Rev.,76, 1232 (1949).

    Google Scholar 

  3. M. Kac and J. C. Ward, Phys. Rev.,88, 1332 (1952).

    Google Scholar 

  4. H. S. Green and C. A. Hurst, Order-Disorder Phenomena, Interscience, New York (1964).

    Google Scholar 

  5. B. M. McCoy and T. T. Wu. The Two-Dimensional Ising Model, Cambridge, Mass. (1973).

  6. F. A. Berezin, Usp. Mat. Nauk,24, 3 (1969).

    Google Scholar 

  7. V. N. Popov, Functional Integrals in Quantum Field Theory and Statistical Physics [in Russian], Atomizdat, Moscow (1976).

    Google Scholar 

  8. E. S. Fradkin and D. M. Shteingradt, Nuovo Cimento A,47, 115 (1978).

    Google Scholar 

  9. I. V. Polubarinov, “On transformation of sums in Ising model,” Preprint E17-84-413 [in English], JINR, Dubna (1984).

    Google Scholar 

  10. V. N. Plechko, “A method of the ordered Grassmann factors in the Ising model,” Preprint E17-84-23 [in English], JINR, Dubna (1984); V. N. Plechko, Dokl. Akad. Nauk SSSR, 281, 834 (1985).

    Google Scholar 

  11. B. N. Valuev, “Application of the Clifford algebra to the solution of the Ising-Onsager problem,” in: Lectures for Young Scientists, No. 14 [in Russian], Soobscheniya (Communication) R17-11020, JINR, Dubna (1977).

    Google Scholar 

  12. S. Samuel, J. Math. Phys.,21, 2806 (1980).

    Google Scholar 

  13. M. Srednicki, Phys. Rev. D,21, 2878 (1980); E. Fradkin, M. Srednicki, and L. Susskind, Phys. Rev. D,21, 2885 (1980).

    Google Scholar 

  14. C. Itzykson, Nucl. Phys. B,210[FS6], 448 (1982).

    Google Scholar 

  15. V. V. Bazhanov and Yu. G. Stroganov, Nucl. Phys. B,230[FS10], 435 (1984).

    Google Scholar 

  16. K. Huang, Statistical Mechanics, New York (1963).

  17. A. Isihara, Statistical Physics, Academic Press, New York (1971).

    Google Scholar 

  18. R. P. Feynman, Lectures on Statistical Mechanics, Benjamin, New York (1971).

    Google Scholar 

  19. F. A. Berezin, The Method of Second Quantization, New York (1966).

Download references

Authors
  1. V. N. Plechko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Joint Institute for Nuclear Research, Dubna. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 64, No. 1, pp. 150–162, July, 1985.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Plechko, V.N. Simple solution of two-dimensional ising model on a torus in terms of Grassmann integrals. Theor Math Phys 64, 748–756 (1985). https://doi.org/10.1007/BF01017042

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01017042

Keywords

Search

Navigation