Abstract
Monte Carlo computer simulations have long been used to obtain information on the behavior of thermodynamic systems. The method has the advantages of being applicable to a very large class of models and of using only systematically improvable approximations (finite size of system, statistical errors, etc.). However, in the critical region, finite-size effects mask the critical singularities, and put severe practical limits onto the accuracy to which the true critical behavior can be determined. By combining Monte Carlo simulations with a real-space renormalization-group analysis, a large increase in efficiency and accuracy can be achieved—without the uncertainties of the usual truncation approximations. The methods are illustrated by explicit calculations on models exhibiting critical and tricritical behavior.
Similar content being viewed by others
References
K. Binder, p. 1 inMonte Carlo Methods in Statistical Physics, Vol. 7, K. Binder, ed. (Springer, Berlin, 1979).
Th. Niemeijer and J. M. J. van Leeuwen, inPhase Transformations and Critical Phenomena, Vol. 6, C. Domb and M. S. Green, eds. (Academic Press, New York, 1976).
S. K. Ma,Phys. Rev. Lett. 37:461 (1976).
R. H. Swendsen, Monte Carlo renormalization, inReal-Space Renormalization, Vol. 30, p. 57, Th. W. Burkhardt and J. M. J. van Leeuwen, eds., Topics in Current Physics (Springer, Berlin, 1982).
R. H. Swendsen, Monte Carlo renormalization group, inPhase Transitions: Cargese 1980, p. 395, M. Levy, J.-C. Le Guillou, and J. Zinn-Justin, eds. (Plenum, New York, 1982).
K. G. Wilson and R. H. Swendsen, unpublished.
K. G. Wilson, Lectures at Les Houches, France, 1980.
K. G. Wilson,Rev. Mod. Phys. 47:773 (1975).
D. P. Landau and R. H. Swendsen,Phys. Rev. Lett 46:1437 (1981).
R. J. Baxter,Ann. Phys. (NY) 70:193 (1972).
R. H. Swendsen and S. Krinsky,Phys. Rev. Lett. 43:177 (1979).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Swendsen, R.H. Monte Carlo renormalization group. J Stat Phys 34, 963–973 (1984). https://doi.org/10.1007/BF01009451
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01009451