Abstract
We study the critical behaviour of the ferromagnetic Potts Model on families of fractal lattices called Sierpinski Carpets and Sierpinski Pastry Shells. We find the influence of geometrical parameters on critical temperature and thermal exponents, which confirms lacunarity as a relevant geometrical parameter in the definition of universality classes. We distinguish the inner surface structure from the bulk and study the influence of both structures independently. The phase diagram for the Pastry Shell family exhibit a crossover between bulk and surface behaviour which shows the increasing importance of the surface bonds on the full fractal geometry as the fractal dimension or the lacunarity is lowered.
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Riera, R., Chaves, C.M. Fractal geometries and Potts Model behaviour. Z. Physik B - Condensed Matter 62, 387–396 (1986). https://doi.org/10.1007/BF01313462
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DOI: https://doi.org/10.1007/BF01313462