2014/02/28 by A. I. Sokolov, M. A. Nikitina · 1 citation
Mathematics · Physics and Astronomy · #Critical exponent #Exponent #Mathematical physics #Mathematics #Phase transition #Physics #Quantum chromodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #Resummation #Scientific Research and Discoveries #Superfluidity #Theoretical and Computational Physics #cond-mat.stat-mech #hep-lat #hep-ph #hep-th
paper · pdf · doi:10.1016/j.physa.2015.10.036
published as Physica A, 444, 177 (2016) · 11 pages, 4 tables; numerical estimates revised, text rewritten
arxiv created 2014/03/31 · openalex publication_date 2015/10/23 · arxiv updated 2016/03/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Pseudo-ε expansions (τ-series) for critical exponents of 3D XY model describing λ-transition in liquid helium are derived up to τ6 terms. Numerical estimates extracted from the τ-series obtained using Padé-Borel resummation technique, scaling relations and seven-loop (τ7) estimate for the Fisher exponent η are presented including those for exponents α and ν measured in experiments with record accuracy. For the exponent α the procedure argued to be most reliable gives α= -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-ε 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.