Abstract
We specialize to then-component cubic model the subgraph break-collapse method which we recently developed for theZ(λ) model. The cubic model has less symmetry than the Potts model, for which the method was originally developed, but nevertheless it is still possible to reduce considerably the computational complexity of the generalZ(λ) model. Our recursive algorithm is similar, forn=2, to the break-collapse method for theZ(4) model proposed by Mariz and co-workers. It allows the exact calculation for the partition function and correlation functions forn-component cubic clusters, withn as a variable, without the need to examine all of the spin configurations. An important application is therefore in real-space renormalization-group calculations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Kim, P. M. Levy, and L. F. Uffer,Phys. Rev. B 12:989 (1975).
A. Aharony,J. Phys. A: Math. Gen. 10:389 (1977).
D. Kim and P. M. Levy,Phys. Rev. B 12:5105 (1975).
D. Kim, P. M. Levy, and J. J. Sudano,Phys. Rev. B 13:2054 (1976).
H. J. Hilhorst,Phys. Lett. 56A:153 (1976).
E. Domany and E. K. Riedel,Phys. Rev. B 19:5817 (1979).
B. Nienhuis, E. K. Riedel, and M. Schick,Phys. Rev. B 27:5625 (1983).
R. Badke, P. Reinicke, and V. Rittenberg,J. Phys. A: Math. Gen. 18:653 (1985).
R. Badke,Phys. Lett. A 119:365 (1987).
C. Tsallis, A. M. Mariz, A. Stella, and L. R. da Silva,J. Phys. A: Math. Gen. 22 (1990).
A. C. N. de Magalhães and J. W. Essam,J. Phys. A: Math. Gen. 22:2549 (1989).
A. C. N. de Magalhães and J. W. Essam,J. Phys. A: Math. Gen. 21:473 (1988).
A. M. Mariz, C. Tsallis, and P. Fulco,Phys. Rev. B 32:6055 (1985).
A. M. Mariz, A. C. N. de Magalhães, L. R. da Silva, and C. Tsallis, to be published.
C. Tsallis,Phys. Rep. Physica A 319 (1990).
E. P. da Silva, C. Tsallis, and A. M. Mariz, to be published.
N. Biggs,Math. Proc. Camb. Phil. Soc. 80:429 (1976).
N. Biggs,Interaction Models (Cambridge University Press, Cambridge, 1977).
F. C. Alcaraz and C. Tsallis,J. Phys. A: Math. Gen. 15:587 (1982).
J. W. Essam and C. Tsallis,J. Phys. A: Math. Gen. 19:409 (1986).
J. Ashkin and E. Teller,Phys. Rev. 64:178 (1943).
C. Tsallis and S. V. F. Levy,Phys. Rev. Lett. 47:950 (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
de Magalhães, A.C.N., Essam, J.W. Then-component cubic model and flows: Subgraph break-collapse method. J Stat Phys 58, 1059–1082 (1990). https://doi.org/10.1007/BF01026563
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01026563