Hamiltonian formulation of bond percolation: an alternative derivation
- 1 September 1978
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 11 (9) , 1803-1806
- https://doi.org/10.1088/0305-4470/11/9/014
Abstract
An alternative derivation of the relationship between bond percolation and the Ashkin-Teller-Potts model, discovered by Kastelyn and Fourtuin (1972), is presented. The derivation is in terms of a correlated bond expansion of standard form. A class of percolation models related to the general p-state model is defined, and a relationship between bond density and internal energy is derived. The nature of the p=1 percolation limit and its correlation function are also discussed.Keywords
This publication has 10 references indexed in Scilit:
- Site-cluster distributions and equation of state for the bond percolation modelPhysical Review B, 1977
- Renormalization of the Potts modelJournal of Physics A: General Physics, 1976
- On the critical behaviour of the s-states Ashkin-Teller-Potts modelPhysics Letters A, 1976
- Critical properties of two tensor models with application to the percolation problemPhysical Review B, 1976
- Percolation problems and the Potts modelPhysics Letters A, 1976
- Renormalization-Group Approach to Percolation ProblemsPhysical Review Letters, 1975
- Three-spin-state generalized Ising modelJournal of Physics C: Solid State Physics, 1974
- On the random-cluster modelPhysica, 1972
- Some generalized order-disorder transformationsMathematical Proceedings of the Cambridge Philosophical Society, 1952
- Statistics of Two-Dimensional Lattices with Four ComponentsPhysical Review B, 1943