The method of Borel resummation is used to obtain an accurate representation of renormalization-group functions of the n -vector model within the minimal renormalization scheme. This permits to relate the nonuniversal critical behaviour of different quantities well away from criticality. The results can be used to estimate the range of applicability of the n -vector model. Application to the λ-transition of 4 He explains the measured effective exponent of the superfluid density along the λ-line.The method of Borel resummation is used to obtain an accurate representation of renormalization-group functions of the n -vector model within the minimal renormalization scheme. This permits to relate the nonuniversal critical behaviour of different quantities well away from criticality. The results can be used to estimate the range of applicability of the n -vector model. Application to the λ-transition of 4 He explains the measured effective exponent of the superfluid density along the λ-line.

Europhysics Letters (EPL)Feb 15, 198767 citations

Dynamic Critical Behavior Near the Superfluid Transition in H3e−H4e Mixtures in Two Loop Order

R. Folk, G. Moser

We calculated in two loop order the field theoretic renormalization group functions taking into account the decomposition of the dynamical vertex functions into the static vertex functions and genuine dynamical parts. The observation of this nonperturbative structure simplifies the theoretical expressions obtained by perturbation theory considerably and makes tractable a complete two loop calculation of the critical dynamics near the superfluid transition of 3He-4He mixtures (model F'). As a result, we obtain various transport coefficients, which govern the nonasymptotic and nonuniversal temperature dependence. We also correct long-standing results for the critical dynamics of the superfluid transition in pure 4He (model F) and for the dynamics of structural or magnetic phase transitions (model C).We calculated in two loop order the field theoretic renormalization group functions taking into account the decomposition of the dynamical vertex functions into the static vertex functions and genuine dynamical parts. The observation of this nonperturbative structure simplifies the theoretical expressions obtained by perturbation theory considerably and makes tractable a complete two loop calculation of the critical dynamics near the superfluid transition of 3He-4He mixtures (model F'). As a result, we obtain various transport coefficients, which govern the nonasymptotic and nonuniversal temperature dependence. We also correct long-standing results for the critical dynamics of the superfluid transition in pure 4He (model F) and for the dynamics of structural or magnetic phase transitions (model C).

Physical Review LettersAug 27, 200215 citations

Renormalization-group flow equations of modelF

V. Dohm

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 \ensuremath{\lambda} transition of $^{4}\mathrm{He}$ at various pressures. Predictions are made for the bulk thermal conductivity very close to ${\mathit{T}}_{\ensuremath{\lambda}}$ 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 \ensuremath{\lambda} line of $^{4}\mathrm{He}$ .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 \ensuremath{\lambda} transition of $^{4}\mathrm{He}$ at various pressures. Predictions are made for the bulk thermal conductivity very close to ${\mathit{T}}_{\ensuremath{\lambda}}$ 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 \ensuremath{\lambda} line of $^{4}\mathrm{He}$.

Physical review. B, Condensed matterAug 1, 199165 citations

^{4}\mathrm{He}

at various pressures. Predictions are made for the bulk thermal conductivity very close to ${\mathit{T}}_{\ensuremath{\lambda}}$ 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 \ensuremath{\lambda} line of

^{4}\mathrm{He}