Critical Exponents of Superfluid Helium and Pseudo-$\epsilon$ Expansion

Abstract

Pseudo-$\epsilon$ expansions ($\tau$-series) for critical exponents of 3D XY model describing $\lambda$-transition in liquid helium are derived up to ${\tau }^6$ terms. Numerical estimates extracted from the $\tau$-series obtained using Padé-Borel resummation technique, scaling relations and seven-loop (${\tau }^7$) estimate for the Fisher exponent $\eta$ are presented including those for exponents $\alpha$ and $\nu$ measured in experiments with record accuracy. For the exponent $\alpha$ the procedure argued to be most reliable gives $\alpha =-0.0117$. This number is very close to the most accurate experimental values differing appreciably from the results of numerous lattice and field-theoretical calculations. It signals that the pseudo-$\epsilon$ expansion is a powerful tool robust enough to evaluate critical exponents with very small absolute error. The arguments in favour of such a robustness are presented.

arXiv comment11 pages, 4 tables; numerical estimates revised, text rewritten

References in corpus (20)

• Critical Phenomena and Renormalization-Group Theory
• Critical Exponents of the N-vector model
• Critical behavior of the three-dimensional XY universality class
• The critical exponents of the superfluid transition in He4
• Specific Heat of Liquid Helium in Zero Gravity very near the Lambda Point
• Critical exponents for 3D O(n)-symmetric model with n > 3
• Seven-Loop Critical Exponents from Strong-Coupling phi^4-Theory in Three Dimensions
• High precision Monte Carlo study of the 3D XY-universality class
• High Precision Measurement of the Thermal Exponent for the Three-Dimensional XY Universality Class
• Pseudo--epsilon expansion of six--loop renormalization group functions of an anisotropic cubic model
• On the criticality of frustrated spin systems with noncollinear order
• Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation
• Harmonic crossover exponents in O(n) models with the pseudo-epsilon expansion approach
• Theory and Satellite Experiment for Critical Exponent alpha of lambda-Transition in Superfluid Helium
• Critical Exponents from Five-Loop Strong-Coupling phi^4-Theory in 4- epsilon Dimensions
• Critical Exponents in Two Dimensions and Pseudo-ε Expansion
• Pseudo-$\epsilon$ Expansion and Renormalized Coupling Constants at Criticality
• Pseudo-epsilon expansion and the two-dimensional Ising model
• On the Critical Exponents for the Λ-Transition in Liquid Helium
• Fisher Exponent from Pseudo-$\epsilon$ Expansion

Cited by in corpus (7)

• Carving out OPE space and precise $O(2)$ model critical exponents
• Quantum critical properties of Bose-Hubbard models
• Effective potential of the three-dimensional Ising model: the pseudo-$\epsilon$ expansion study
• Anisotropy of a Cubic Ferromagnet at Criticality
• The modification of exponents in the Ginzburg-Sobyanin theory of superfluidity
• Universal effective couplings of the three-dimensional $n$-vector model and field theory
• Critical Exponents of the O(N)-symmetric ${\varphi }^4$ Model from the \boldmath{\large{ ${\epsilon }^7$}} Hypergeometric-Meijer Resummation