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 \ensuremath{\epsilon}=4-d. Calculations for the exponents and amplitude ratios are given correct to O(${\mathrm{\ensuremath{\epsilon}}}^{2}$) and O(\ensuremath{\epsilon}), respectively, for the heat capacity (both above and below ${\mathit{T}}_{\mathit{C}}$) and for the susceptibility (above ${\mathit{T}}_{\mathit{C}}$). The new amplitude ratios associated with dilution effects are calculated for both the first-order (associated with critical exponents ${\mathrm{\ensuremath{\Delta}}}_{1}$=-\ensuremath{\alpha},${\mathrm{\ensuremath{\Delta}}}_{2}$=\ensuremath{\omega}\ensuremath{\nu}) and the second-order (associated with critical exponents ${\mathrm{\ensuremath{\Delta}}}_{3}$=-2\ensuremath{\alpha},${\mathrm{\ensuremath{\Delta}}}_{4}$=-\ensuremath{\alpha}+\ensuremath{\omega}\ensuremath{\nu},${\mathrm{\ensuremath{\Delta}}}_{5}$=2\ensuremath{\omega}\ensuremath{\nu}) corrections to scaling. The diluted O(m) model has the feature that the correction to scaling associated with \ensuremath{\Vert}t${\mathrm{\ensuremath{\Vert}}}^{{\mathrm{\ensuremath{\Delta}}}_{2}}$, which is formally of first order with respect to the perturbative coupling constants, becomes negligible for sufficiently small \ensuremath{\Vert}t\ensuremath{\Vert} relative to \ensuremath{\Vert}t${\mathrm{\ensuremath{\Vert}}}^{{\mathrm{\ensuremath{\Delta}}}_{3}}$, 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. \textcopyright{} 1996 The American Physical Society.