Renormalization-Group Calculations of Divergent Transport Coefficients at Critical Points

Abstract

Recursion relations correct to lowest order in $\ensuremath{\epsilon}=4\ensuremath{-}d$ are obtained for simple models representing the critical dynamics of a binary liquid, a Heisenberg antiferromagnet, superfluid helium, and related systems. The exponents for the divergences of the transport coefficients satisfy the "scaling" relations predicted by mode-mode coupling theory. The viscosity of the binary liquid is predicted to diverge as ${k}^{\ensuremath{-}\frac{\ensuremath{\epsilon}}{19}}$ near $d=4$, which is a new result.