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Prog. Theor. Phys. Vol. 54 No. 4 (1975) pp. 1067-1076

Temperature-Dependent Percolation Problem in the Bethe Lattice

Takashi Odagaki

Department of Chemistry, Faculty of Science, Kyoto University, Kyoto 606

(Received April 11, 1975)

Abstract:

The temperature-dependent percolation problem in a lattice gas is solved rigorously for the Bethe lattice. Explicit expressions are given for the probability of a site belonging to a finite cluster, the probability (percolation probability) of a site belonging to an infinite cluster and the mean finite cluster size. The critical percolation density is an increasing function of temperature for the attractive interaction and a decreasing function for the repulsive interaction. The critical index of the percolation probability is unity, independent of temperature.

URL : http://ptp.ipap.jp/link?PTP/54/1067/
DOI : 10.1143/PTP.54.1067

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References:

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Citing Article(s) :

1. Journal of the Physical Society of Japan 69 (2000) pp. 3308-3314 :

   Concentration Fluctuation and Salt-Induced Percolation in 1-Propanol Aqueous Solution

   Masakatsu Misawa and Katsumi Yoshida

2. Progress of Theoretical Physics Vol. 79 No. 5 (1988) pp. 1080-1094 :

   Percolation Problem Describing ±J Ising Spin Glass System

   Yasuhiro Kasai and Ayao Okiji

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