Renormalization-Group Calculations of Divergent Transport Coefficients at Critical Points

Abstract

Recursion relations correct to lowest order in $\epsilon =4-d$ 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 $k^{-\frac{\epsilon }{19}}$ near $d=4\mathrm{}$, which is a new result.