On randomly dilute ferromagnetic models

Abstract

The paper considers the I(1/2), H(1/2), and H( infinity ) ferromagnetic models in which there are nonmagnetic impurities distributed at random on the sites of the underlying physical lattice. High temperature power series expansions, which are presented, are analysed by conventional methods to find the Curie temperature Tc(p) and susceptibility exponent gamma (p), where p is the concentration of magnetic elements. The series are analysed for p>1, as well as p<1, thus making contact with the nonselfintersecting chain problem. At p=1, gradients of TC(p)/TC(1) against p, are found, for the face centred cubic lattice, to be 1.05+or-0.02 for I(1/2), 1.15+or-0.01 for H( infinity ) and 1.36+or-0.03 for H(1/2). For the plane triangular lattice, the initial gradient for the I(1/2) model is 1.45+or-0.05. The behaviour found for gamma (p) is rejected as physically implausible, and the implications of its anomalous behaviour are discussed.