“Thermodynamical formalism” for an infinite hierarchy of fractal resistor networks

Preben Alstrøm, Dimitris Stassinopoulos and H.Eugene Stanley

Physica A: Statistical Mechanics and its Applications, 1988, vol. 153, issue 1, 20-46

Abstract: 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).

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:153:y:1988:i:1:p:20-46

DOI: 10.1016/0378-4371(88)90099-4

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