Abstract
In this expanded version of an earlier letter, we consider many computational details that were omitted for want of space. Ford = 2 Ising spins with up to 13 different short-range interactions, we construct the critical surface in the vicinity of (Onsager's) nearest-neighbor (nn) critical point by using the body of the available information on the solvable nn case. We then see if the Monte Carlo renormalization group flows generated from this point do indeed lie on this surface and quantify the errors if they do not.
Similar content being viewed by others
References
K. G. Wilson,Phys. Rev. B 4:3174, 3184 (1971).
K. G. Wilson and J. B. Kogut,Phys. Rep. 12C:75 (1974).
M. E. Fisher, inCritical Phenomena, F. J. W. Hahne, ed. (Lecture Notes in Physics, No. 186, Springer-Verlag, Berlin, 1983).
K. Binder, ed.,Monte Carlo Methods in Statistical Physics, Topics in Current Physics, Vol. 7 (Springer-Verlag, Berlin, 1979).
R. H. Swendsen,Phys. Rev. B 30:3866, 3875 (1984).
R. Gupta and R. Cordery,Phys. Lett. 105A:415 (1984).
G. Murthy and R. Shankar,Phys. Rev. Lett. 54:1110 (1985).
B. McCoy and T. T. Wu,The Two-Dimensional Ising Model (Harvard University Press, Cambridge, Massachusetts, 1973).
C. Itzykson,Nucl. Phys. B210(FS6):448 (1982).
M. Nauenberg and B. Nienhuis,Phys. Rev. Lett. 33:1598 (1974).
D. J. E. Callaway and R. Petronzio, CERN Report No. TH.3806-CERN, 1984 (to be published).
R. B. Griffiths,J. Math. Phys. (N.Y.) 8:484 (1967).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Murthy, G., Shankar, R. Tests for Monte Carlo renormalization studies on Ising models. J Stat Phys 42, 275–288 (1986). https://doi.org/10.1007/BF01127713
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01127713