Polynomial-time approximation algorithms for the ising model

  • Mark Jerrum
  • Alistair Sinclair
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 443)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Binder, K., Monte Carlo investigations of phase transitions and critical phenomena, in Phase Transitions and Critical Phenomena, Volume 5b (C. Domb and M. S. Green eds.), Academic Press, London, 1976, pp. 1–105.Google Scholar
  2. [2]
    Cipra, B., An introduction to the Ising model, American Mathematical Monthly, 94 (1987), pp. 937–959.Google Scholar
  3. [3]
    Diaconis, P. and Stroock D., Geometric bounds for eigenvalues of Markov chains, Technical Report No. 325, Department of Statistics, Stanford University, July 1989.Google Scholar
  4. [4]
    Dyer, M., Frieze, A., and Kannan, R., A random polynomial time algorithm for approximating the volume of convex bodies, Proceedings of the 21st ACM Symposium on Theory of Computing, 1989, pp. 375–381.Google Scholar
  5. [5]
    Feller, W., An introduction to probability theory and its applications, Volume I (3rd edition), John Wiley, New York, 1968.Google Scholar
  6. [6]
    Fisher, M. E., On the dimer solution of planar Ising models, Journal of Mathematical Physics 7 (1966), pp. 1776–1781.Google Scholar
  7. [7]
    Ising, E., Beitrag zur Theorie des Ferromagnetismus, Zeitschrift für Physik 31 (1925), pp. 253–258.Google Scholar
  8. [8]
    Jerrum, M. R. and Sinclair, A. J., Approximating the permanent, SIAM Journal on Computing 18 (1989), pp. 1149–1178.Google Scholar
  9. [9]
    Jerrum, M. R. and Sinclair, A. J., Polynomial-time approximation algorithms for the Ising model, Internal Report CSR-1-90, Department of Computer Science, University of Edinburgh (submitted to Journal of the ACM).Google Scholar
  10. [10]
    Jerrum, M. R., Valiant, L. G., and Vazirani, V. V., Random generation of combinatorial structures from a uniform distribution, Theoretical Computer Science 43 (1986), pp. 169–188.Google Scholar
  11. [11]
    Karp, R. M. and Luby, M., Monte-Carlo algorithms for enumeration and reliability problems, Proceedings of the 24th IEEE Symposium on Foundations of Computer Science, 1983, pp. 56–64.Google Scholar
  12. [12]
    Kasteleyn, P. W., Dimer statistics and phase transitions, Journal of Mathematical Physics 4 (1963), pp. 287–293.Google Scholar
  13. [13]
    Kirkpatrick, S., Gelatt, C., and Vecchi, M., Optimisation by simulated annealing, Science 220 (May 1983), pp. 671–680.Google Scholar
  14. [14]
    Lenz, W., Beitrag zum Verständnis der magnetischen Erscheinungen in festen Körpern, Zeitschrift für Physik 21 (1920), pp. 613–615.Google Scholar
  15. [15]
    Newell, G. F. and Montroll, E. W., On the theory of the Ising model of ferromagnetism, Reviews of Modern Physics 25 (1953), pp. 353–389.Google Scholar
  16. [16]
    Sinclair, A., Randomised Algorithms for Counting and Generating Combinatorial Structures, Ph.D. Thesis, University of Edinburgh, 1988.Google Scholar
  17. [17]
    Sinclair, A. and Jerrum, M., Approximate counting, uniform generation, and rapidly mixing Markov chains, Information and Computation 82 (1989), pp. 93–133.Google Scholar
  18. [18]
    Welsh, D. J. A., The computational complexity of some classical problems from statistical physics, in Disorder in Physical Systems, Oxford University Press, February 1990, pp. 307–321.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Mark Jerrum
    • 1
  • Alistair Sinclair
    • 1
  1. 1.Department of Computer ScienceUniversity of EdinburghEdinburghScotland

Personalised recommendations