J. Phys. I France
Volume 2, Numéro 1, January 1992
Page(s) 41 - 54
DOI: 10.1051/jp1:1992117
J. Phys. I France 2 (1992) 41-54

Antiferromagnetic Potts model on Sierpinski carpets

A Bakchich1, 2, A. Benyoussef2 and N. Boccara3, 4

1  Département de Physique, Faculté des Sciences, El-Jadida, Morocco
2  Laboratoire de Magnétisme, Faculté des Sciences, B.P. 1014, Rabat, Morocco
3  Institut de Recherche Fondamentale, DPh-G/PSRM, CEN-Saclay, 91191 Gif-sur-Yvette Cedex, France
4  Dept. of Physics, Box 4348, UIC, Chicago, IL 60680, U.S.A.

(Received 14 January 1991, revised 29 August 1991, accepted 20 September 1991)

An approximate real-space renormalisation group method, based on the Migdal-Kadanoff recursion relations, is used to study the critical properties of the pure and diluted q-state antiferromagnetic Potts model on Sierpinski carpets. Fixed points and phase diagrams are calculated for both large and small lacunarity carpets family. The pure model has phase transitions at finite temperatures and critical behaviour is observed for q less than a cutoff value q0. We determine the value of q0, the percolation concentration $p_{\rm c}$ for the diluted model, and the critical exponents, and we investigate their dependence on various geometrical characteristics of the fractal.

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