Renormalization-group flow equations of modelF

The dynamic renormalization-group flow equations for model F of Halperin, Hohenberg, and Siggia [Phys. Rev. B 13, 1299 (1976)] are calculated by means of renormalized field theory within the minimal-renormalization scheme up to two-loop order. These equations are combined with the Borel-resummation results for the static renormalization-group functions computed by Schloms and Dohm. The corresponding static fixed point destabilizes the dynamic-scaling fixed point in two-loop order. The nonuniversal initial values of the static and dynamic flow equations are identified for the λ transition of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at various pressures. Predictions are made for the bulk thermal conductivity very close to ${\mathit{T}}_{\lambda }$ where the departures from dynamic scaling should be observable. Effective static and dynamic parameters are computed that can be applied to other critical phenomena above and below the λ line of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.