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

TL;DR

The paper develops a perturbation theory for the critical viscosity exponent in fluids, suggesting higher-loop effects are negligible and providing a close approximation for the exponent value.

Contribution

It introduces a loopwise perturbation approach for the critical viscosity exponent and argues that beyond two loops, effects are insignificant.

Findings

Critical viscosity exponent approximated as 0.0685

Higher-loop contributions are negligible

Perturbation theory confirms previous estimates

Abstract

We arrange the loopwise perturbation theory for the critical viscosity exponent $x_{\eta}$, which happens to be very small, as a power series in $x_{\eta}$ 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 $x_{\eta}=\frac{8}{15 \pi^2}(1+\frac{8}{3 \pi^2})\simeq 0.0685$.