Critical Viscosity Exponent for Fluids: What Happend to the Higher Loops

Abstract

We arrange the loopwise perturbation theory for the critical viscosity exponent $x_η$, which happens to be very small, as a power series in $x_η$ itself and argue that the effect of loops beyond two is negligible. We claim that the critical viscosity exponent should be very closely approximated by $x_η=\frac{8}{15 π^2}(1+\frac{8}{3 π^2})\simeq 0.0685$.