Universal correction to scaling amplitude ratios for inhomogeneous ferromagnets with continuous symmetry

Abstract

Critical exponents and amplitude ratios for corrections to the scaling limit are calculated for a randomly diluted, weakly inhomogeneous O(m) Heisenberg model in an expansion in =4-d. Calculations for the exponents and amplitude ratios are given correct to O(2) and O(), respectively, for the heat capacity (both above and below TC) and for the susceptibility (above TC). The new amplitude ratios associated with dilution effects are calculated for both the first-order (associated with critical exponents 1=-, N2=N) and the second-order (associated with critical exponents 3=-2, 4=-+N, 5=2N) corrections to scaling. The diluted O(m) model has the feature that the correction to scaling associated with |t| relative to |t|(2), which is formally of first order with respect to the perturbative coupling constants, becomes negligible for sufficiently small |t| relative to |t|(3), which is formally of higher order in the perturbative coupling constant expansion. The implications of these results for the analysis of experimental data are discussed