Mean field theory of percolation with application to surface effects
- 1 August 1981
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 14 (8) , 1993-2008
- https://doi.org/10.1088/0305-4470/14/8/024
Abstract
A probabilistic formulation of mean field theory for percolation in a general medium is given. The theory covers the whole density range and, above the critical density, provides the necessary generalisation of the random walk approximation. Application to surface percolation enables the calculation of scaling functions and critical exponents for the ordinary, surface, special and extraordinary transitions considered by previous authors to the context of ferromagnetism.Keywords
This publication has 11 references indexed in Scilit:
- Percolation theoryReports on Progress in Physics, 1980
- Surface effects and percolation : the repulsive caseJournal de Physique Lettres, 1980
- Critical behaviour of semi-infinite systemsJournal of Physics A: General Physics, 1977
- Percolation theory in a gasJournal of Physics A: General Physics, 1977
- A real-space renormalization group for site and bond percolationJournal of Physics C: Solid State Physics, 1977
- Critical phenomena in semi-infinite systems. II. Mean-field theoryPhysical Review B, 1975
- Scaling Theory for Finite-Size Effects in the Critical RegionPhysical Review Letters, 1972
- Surface Effects in Magnetic Crystals near the Ordering TemperaturePhysical Review B, 1971
- Bounded and Inhomogeneous Ising Models. I. Specific-Heat Anomaly of a Finite LatticePhysical Review B, 1969
- Correlations in Ising Ferromagnets. II. External Magnetic FieldsJournal of Mathematical Physics, 1967