Journal of Statistical Physics

, Volume 8, Issue 4, pp 309–333 | Cite as

Two-component ising chain with nearest-neighbor interaction

  • F. T. Lee
  • E. W. Montroll
  • Lee-po Yu
Articles

Abstract

The one-dimensional, two-component linear Ising chain with nearest-neighbor interaction is formulated by using the transfer matrix method, with emphasis placed on the case in which the two components are randomly distributed along the chain. Certain recurrence formulas appear such that themth-order partition function of one of the components is dependent on the lower-order ones. The algorithm provides a working basis for discussing the thermodynamic and magnetic functions with various concentrations of one of the components. An exact expression for the partition function is derived for a linear chain which is composed of a periodic distribution of the two components. The construction of a periodic sequence which would approximate a random distribution of the two components is briefly discussed.

Key words

Ising model disordered system one-dimensional chain 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. Ising,Z. Phys. 31:253 (1925).Google Scholar
  2. 2.
    E. W. Montroll and G. S. Goel,Biopolymers 4:855 (1966).Google Scholar
  3. 3.
    E. W. Montroll and Lee-po Yu,Localized Excitations in Solids, Plenum Press, New York, 1968, p. 745.Google Scholar
  4. 4.
    W. Hamilton and G. Pake,J. Chem. Phys. 39:2694 (1963).Google Scholar
  5. 5.
    A. S. Edelstein,J. Chem. Phys. 40:488 (1964).Google Scholar
  6. 6.
    J. W. Stout and R. C. Chisholm,J. Chem. Phys. 36:979 (1962).Google Scholar
  7. 7.
    R. A. Hunt and D. J. Newman,J. Phys. C Sol. St. Phys. 3:2233 (1970).Google Scholar
  8. 8.
    C. Fan and B. M. McCoy,Phys. Rev. 182:614 (1969).Google Scholar
  9. 9.
    H. Falk,Phys. Rev. 151:304 (1966).Google Scholar
  10. 10.
    G. F. Newell and E. W. Montroll,Rev. Mod. Phys. 25:353 (1953).Google Scholar
  11. 11.
    M. P. Kawatra and L. J. Kijewski,Phys. Rev. 183:291 (1969).Google Scholar
  12. 12.
    N. S. Goel Thesis, University of Maryland, 1965.Google Scholar
  13. 13.
    R. Brout,Phys. Rev. 115:824 (1959).Google Scholar

Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • F. T. Lee
    • 1
  • E. W. Montroll
    • 2
  • Lee-po Yu
    • 3
  1. 1.Physics DepartmentUniversity of MalayaKuala LumpurMalaysia
  2. 2.Institute for Fundamental Studies, Department of Physics and AstronomyUniversity of RochesterRochester
  3. 3.National Institutes of HealthWashington, D. C.

Personalised recommendations