“Thermodynamical formalism” for an infinite hierarchy of fractal resistor networks
A thermodynamical formalism for resistor networks is developed in order to extract full information on the multifractal scaling structure. We introduce a matrix representation and study the moments of the voltage distribution Z̃(β) = ∑i=1N|Vi|β α N -F̄(β) where N is the number of resistors. We find a generic phase transition at β = βc = -1. Also, we develop a transfer matrix technique which determines all even positive moments. The thermodynamical formalism is applied to the Hilfer-Blumen hierarchy of generalized Sierpinski gasket fractal networks, and the crossover from fractal to lattice behavior is studied. At this crossover we find a sharp phase transition in the second moment (β = 2).
Year of publication: |
1988
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Authors: | Alstrøm, Preben ; Stassinopoulos, Dimitris ; Stanley, H. Eugene |
Published in: |
Physica A: Statistical Mechanics and its Applications. - Elsevier, ISSN 0378-4371. - Vol. 153.1988, 1, p. 20-46
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Publisher: |
Elsevier |
Saved in:
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