Mean-field renormalisation group transformations for geometric phase transitions
- 21 April 1983
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 16 (6) , 1279-1287
- https://doi.org/10.1088/0305-4470/16/6/022
Abstract
It is shown that the mean-field renormalisation group technique of Indekeu et al. (1982) may be applied directly to the self-avoiding walk (SAW) and percolation problems (without reference to the n to 0 limit of interacting spin systems). Numerical results for the SAW and bond and site percolation (both directed and undirected) problems on the square lattice, obtained by using a variety of small cells, are reported. An isotropic transformation for the percolation problems on the d-dimensional hypercubic lattice is also discussed.Keywords
This publication has 18 references indexed in Scilit:
- Directed percolation: mean field theory and series expansions for some two-dimensional latticesJournal of Physics A: General Physics, 1983
- Renormalisation group recursions by mean-field approximationsJournal of Physics A: General Physics, 1982
- Mean field theory of percolation with application to surface effectsJournal of Physics A: General Physics, 1981
- Directed percolation: a finite-size renormalisation group approachJournal of Physics A: General Physics, 1981
- Percolation theoryReports on Progress in Physics, 1980
- Series expansions for the directed-bond percolation problemJournal of Physics C: Solid State Physics, 1977
- Percolation Phenomena in Higher Dimensions: Approach to the Mean-Field LimitPhysical Review Letters, 1976
- Solutions of Flexible Polymers. Neutron Experiments and InterpretationMacromolecules, 1975
- The Lagrangian theory of polymer solutions at intermediate concentrationsJournal de Physique, 1975
- Exponents for the excluded volume problem as derived by the Wilson methodPhysics Letters A, 1972