Scaling Theory of Potts Model and Fractal Dimensions
نویسندگان
چکیده
منابع مشابه
Fractal Dimensions and Corrections to Scaling for Critical Potts Clusters
Renormalization group and Coulomb gas mappings are used to derive theoretical predictions for the corrections to the exactly known asymptotic fractal masses of the hull, external perimeter, singly connected bonds and total mass of the FortuinKasteleyn clusters for two-dimensional q-state Potts models at criticality. For q = 4 these include exact logarithmic (as well as log log) corrections.
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Fortuin–Kastelyn clusters in the critical Q-state Potts model are conformally invariant fractals. We obtain simulation results for the fractal dimension of the complete and external (accessible) hulls for Q = 1, 2, 3, and 4, on clusters that wrap around a cylindrical system. We find excellent agreement between these results and theoretical predictions. We also obtain the probability distributio...
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1. Ya, G, Sinai, Theory of Phase Transitions, Rigorous Results (Acad, Kiado, Budapest, 1982), 2, S, E. Burkov, J, Phys, (Paris) 46:317-327 (1985). 3, R. L. Dobrushin, Teor, Veroyat, Primenenie 17(4):619-639 (1972), 4, M, Aizenman, Commun, Math. Phys, 73:83-94 (1980), 5, Y. Higuchi, Random Fields, Colloquis Math, Soc. Janos Bolyai 271:517-534 (1981), 6, R. L. Dobrushin and B. B. Shlosman, Sov, S...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics
سال: 1985
ISSN: 0033-068X,1347-4081
DOI: 10.1143/ptp.74.916