Advertisement

Solution of the Dimer Problem by the Transfer Matrix Method

  • Elliott H. Lieb
Chapter

Abstract

It is shown how the monomer-dimer problem can be formulated in terms of a transfer matrix, and hence in terms of simple spin operators as was originally done for the Ising problem. Thus, we rederive the solution to the pure dinier problem without using Pfaffians. The solution is extremely simple once one sees how to formulate the transfer matrix.

Keywords

Ising Model Transfer Matrix Transfer Matrix Method Cyclic Boundary Condition Versus Bond 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference

  1. 1.
    L. Onsager, Phys. Rev. 65, 117 (1944).MathSciNetADSMATHCrossRefGoogle Scholar
  2. 2.
    We make no attempt to give a complete bibliography because an excellent one is given in H. S. Green and C. A. Hurst, Order-Disorder Phenomena (Interscience Publishers, Inc., New York, 1964 ).Google Scholar
  3. 3.
    M. Kac and J. C. Ward, Phys. Rev. 88, 1332 (1952).ADSMATHCrossRefGoogle Scholar
  4. 4.
    P. W. Kasteleyn, Physica 27, 1209 (1962); J. Math. Phys. 4, 287 (1963); H. N. V. Temperley and M. E. Fisher, Phil. Mag. 6, 1061 (1961); M. E. Fisher, Phys. Rev. 124, 1664 (1961).Google Scholar
  5. 5.
    C. A. Hurst and H. S. Green, J. Chem. Phys. 33, 1059 (1960).MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    T. D. Schultz, D. C. Mattis, and E. H. Lieb, Rev. Mod. Phys. 36, 856 (1964).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Elliott H. Lieb
    • 1
  1. 1.Physics DepartmentNortheastern UniversityBostonUSA

Personalised recommendations