Skip to main content

Continuous exponents of spin correlation functions of inhomogeneous layered ising models

1. Statistical Mechanics and the Riemann Monodromy Problem

  • 435 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 925)

Abstract

In this note we consider the inhomogeneous layered Ising model and we present a general formalism for expressing as a Toeplitz determinant the correlation of two spins in a row possessing reflection symmetry. For the special case where there is one altered row of horizontal bonds E1′ in an otherwise homogeneous lattice we discuss the correlations in detail and show that the critical exponents β and ν depend on E1′.

Keywords

  • Ising Model
  • Transfer Matrix
  • Critical Exponent
  • Recursion Relation
  • Clifford Algebra

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. M. McCoy and T. T. Wu, Phys. Rev. 162, 436 (1967).

    CrossRef  Google Scholar 

  2. B. M. McCoy and T. T. Wu, Phys. Rev. Letts. 21, 549 (1968) and Phys. Rev. 176, 631 (1968).

    CrossRef  Google Scholar 

  3. M. E. Fisher and A. E. Ferdinand, Phys. Rev. Letts. 19, 169 (1967); A. E. Ferdinand and M. E. Fisher, Phys. Rev. 185, 832 (1969).

    CrossRef  Google Scholar 

  4. B. M. McCoy, Phys. Rev. Letts. 23, 383 (1969); Phys. Rev. 188, 1014 (1969).

    CrossRef  Google Scholar 

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

    CrossRef  MathSciNet  Google Scholar 

  6. Some recent work on inhomogeneous Ising lattices has been made by J.H.H. Perk, Phys. Letts. (to be published).

    Google Scholar 

  7. E. Barouch, B.M. McCoy and T.T. Wu, Phys. Rev. Letts 31, 1409 (1973).

    CrossRef  Google Scholar 

  8. Our results are presented in B.M. McCoy and J.H.H. Perk, Phys. Rev. Letts. 44, 840 (1980).

    CrossRef  Google Scholar 

  9. B. Kaufman, Phys. Rev. 76, 1232 (1949); B. Kaufman and L. Onsager, Phys. Rev. 76, 1244 (1949).

    CrossRef  Google Scholar 

  10. J.H.H. Perk and H.W. Capel, Physica 89A, 265 (1977).

    CrossRef  MathSciNet  Google Scholar 

  11. For an explanation of these techniques see “The Two-Dimensional Ising Model” by B.M. McCoy and T. T. Wu, Harvard University Press, Cambridge, Mass. 1973.

    CrossRef  MATH  Google Scholar 

  12. G. Szegö, Communications du Séminaire Mathématique de l'Université de Lund, tome supplémentaire dédié à Marcel Riesz, 1952, p. 228.

    Google Scholar 

  13. T. T. Wu, Phys. Rev. 149, 380 (1966).

    CrossRef  Google Scholar 

  14. T. T. Wu, B.M. McCoy, C.A. Tracy and E. Barouch, Phys. Rev. B 13, 316 (1976).

    CrossRef  Google Scholar 

  15. R. Z. Bariev, Zh. Eksp. Teor. Fiz. 77, 1217 (1979), Sov. Phys. JETP 50, 613 (1979). *** DIRECT SUPPORT *** A00J4399 00002

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

McCoy, B.M., Perk, J.H.H. (1982). Continuous exponents of spin correlation functions of inhomogeneous layered ising models. In: Chudnovsky, D.V., Chudnovsky, G.V. (eds) The Riemann Problem, Complete Integrability and Arithmetic Applications. Lecture Notes in Mathematics, vol 925. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093496

Download citation

  • DOI: https://doi.org/10.1007/BFb0093496

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11483-3

  • Online ISBN: 978-3-540-39152-4

  • eBook Packages: Springer Book Archive