Excitations of Dilute Magnets Near the Percolation Threshold
- 226 Downloads
The random dilution of magnetic crystals with short range interactions provides for experimental investigation of percolation theories, in particular the multiscaling hypothesis for the region close to the percolation point (p = pc, T = 0)[1,2]. Percolation has been intensively studied by series expansion, computer simulation and renormalisation group methods giving numerically well-defined exponents for quantities such as the percolation probability P(p) ∿ (p-pc)βp and the geometric correlation length ξ(p) ∿ p-pc)-ν p, Many experimentally accessible variables, however, such as correlation functions and excitation spectra cannot easily be calculated by formal renormalisation group techniques and are not reliably given by effective medium type theories. It is valuable, then, to develop scaling models consistent with known critical singularities yet simple enough to allow calculation of such experimentally determined quantities.
KeywordsSpin System Percolation Threshold Model Cluster Short Range Interaction Renormalisation Group Method
Unable to display preview. Download preview PDF.
- 1.R.A. Cowley, R.J. Birgeneau, G. Shirane 1979 (These proceedings).Google Scholar
- 4.A.S. Skal and B.I. Shklovskii 1974 Fiz. Tekh. Poluprovdn. 8 1586–92 (Sov. Phys.-Semicond. 8 1029–32).Google Scholar
- 5.P.G. de Gennes 1976 J. Physique 37 L1–2.Google Scholar
- 9.M.J. Stephen and G.S. Grest 1977 Phys. Rev. Lett. 38 567–70.Google Scholar
- 11.T.A.L. Ziman 1979 J.Phys.C: Solid St. Phys. (in press); see also T.A.L. Ziman 1978 D.Phil. Thesis, Oxford University (Unpublished).Google Scholar