Skip to main content
SpringerLink
Log in

Statistical properties of the exact solutions of the one-dimensional φ4-Model

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

We analyse the statistical properties of the exact solutions obtained recently from the minimisation procedure in the one-dimensional φ4-model. Constant, periodic and localised solutions are included in the analysis and their energy spectra found. Subsequently, each class of solutions is examined as to their contributions towards statistical quantities such as the partition function and the specific heat. Information regarding stability and signatures of the individual types of excitations in the system has been obtained.

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. L. D. Landau andE. M. Lifshitz:Statistical Physics (Pergamon, London, 1959).

    MATH  Google Scholar 

  2. V. L. Ginzburg andL. D. Landau:Ž. Ėksp. Teor. Fiz.,20, 1064 (1950).

    MATH  Google Scholar 

  3. S.-K. Ma:Theory of Critical Phenomena (Benjamin, Reading, Mass., 1976).

    MATH  Google Scholar 

  4. J. A. Krumhansl andJ. R. Schrieffer:Phys. Rev. B,11, 3535 (1975).

    Article  ADS  Google Scholar 

  5. W. Dieterich:Adv. Phys.,25, 615 (1976).

    Article  ADS  Google Scholar 

  6. A. R. Bishop andJ. A. Krumhansl:Phys. Rev. B,12, 2824 (1975).

    Article  ADS  Google Scholar 

  7. G. Parisi:Statistical Field Theory (Addison-Wesley, Redwood City, Cal., 1988).

    MATH  Google Scholar 

  8. J. F. Currie, J. A. Krumhansl, A. R. Bishop andS. E. Trullinger:Phys. Rev. B,22, 477 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  9. J. W. Nagele andH. Orland:Quantum Many-Particle Systems (Addison-Wesley, Redwood City, Cal., 1988).

    Google Scholar 

  10. B. Sakita:Quantum Theory of Many-Variable Systems and Fields (World Scientific, Singapore, 1985).

    Book  MATH  Google Scholar 

  11. D. J. Amit:Field Theory, the Renormalization Group and Critical Phenomena (McGraw-Hill, New York, N.Y., 1978).

    Google Scholar 

  12. P. Winternitz, A. M. Grundland andJ. A. Tuszyński:J. Phys. C,21, 4931 (1988).

    Article  ADS  Google Scholar 

  13. L. W. Gruenberg andL. Gunther:Phys. Lett. A,38, 463 (1972).

    Article  ADS  Google Scholar 

  14. A. Michelson:Phys. Rev. B,16, 577 (1977).

    Article  ADS  Google Scholar 

  15. R. M. Hornreich, M. Luban andS. Shtrikman:Phys. Rev. Lett.,35, 1078 (1975).

    Article  ADS  Google Scholar 

  16. W. I. Khan:J. Magn. Magn. Mater.,78, 313 (1989).

    Article  ADS  Google Scholar 

  17. W. Wasilewski:J. Magn. Magn. Mater.,30, 312 (1983).

    Article  ADS  Google Scholar 

  18. S. Aubry:J. Chem. Phys.,64, 3392 (1976).

    Article  ADS  Google Scholar 

  19. C. Kittel:Phys. Rev.,120, 335 (1960).

    Article  MathSciNet  ADS  Google Scholar 

  20. W. A. Barber andG. A. Gehring:J. Phys. C,16, 6415 (1983).

    Article  ADS  Google Scholar 

  21. P. F. Byrd andM. D. Friedmann:Handbook of Elliptic Integral for Engineers and Scientists (Springer-Verlag, Berlin, 1971).

    Book  Google Scholar 

  22. S. E. Trullinger andR. M. De Leonardis:Phys. Rev. A,20, 2225 (1979).

    Article  MathSciNet  ADS  Google Scholar 

  23. A. M. Grundland, E. Infeld, G. Rowlands andP. Winternitz:J. Phys. Condensed Matter,2, 7143 (1990).

    Article  ADS  Google Scholar 

  24. T. Schneider: inSolitons, edited byS. E. Trullinger, V. E. Zakharov andV. L. Pokrovsky (North-Holland, Amsterdam, 1986), p. 389.

    Google Scholar 

  25. J. Rudnick, H. Guo andD. Jasnow:J. Stat. Phys.,41, 353 (1985).

    Article  ADS  Google Scholar 

  26. M. Gajdek andW. Wasilewski:J. Phys. C,18, 3557 (1985).

    Article  ADS  Google Scholar 

  27. R. Szymczak, A. Maziewski andK. Piotrowski:J. Magn. Magn. Mater.,12, 227 (1979).

    Article  ADS  Google Scholar 

  28. G. Ahlers:Physica D,51, 421 (1991).

    Article  ADS  MATH  Google Scholar 

  29. J. T. Stuart andR. C. Di Prima:Proc. R. Soc. London, Ser. A,362, 27 (1978).

    Article  ADS  MATH  Google Scholar 

  30. L. Sirovich andP. K. Newton:Physica D,21, 115 (1986).

    Article  MathSciNet  ADS  Google Scholar 

  31. Y. Kuramoto andT. Yamada:Prog. Theor. Phys.,56, 670 (1976).

    MathSciNet  ADS  Google Scholar 

  32. M. Yamashita:J. Phys. Soc. Jpn.,57, 582 (1988).

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Alberta, T6G 2J1, Edmonton, Alberta, Canada

    M. L. A. Nip & J. A. Tuszyński

Authors
  1. M. L. A. Nip
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. A. Tuszyński
    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

Nip, M.L.A., Tuszyński, J.A. Statistical properties of the exact solutions of the one-dimensional φ4-Model. Nuovo Cim B 109, 507–521 (1994). https://doi.org/10.1007/BF02728392

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02728392

PACS 05.45

PACS 03.20

PACS 63.20.Ry

Search

Navigation