Excitations of Dilute Magnets Near the Percolation Threshold

Abstract

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 = p_c, 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-p_c)^βp and the geometric correlation length ξ(p) ∿ p-p_c)^-νp[3], 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.