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arXiv:2111.04719 · Physics Letters A

The dynamic critical exponent z for 2d and 3d Ising models from five-loop ε expansion

L. Ts. Adzhemyan, Daniil A. Evdokimov, Michal Hnatič, Ella V. Ivanova, Mikhail Vladimirovich Kompaniets, Andrey Kudlis, D.V. Zakharov

Published Nov 30, 2021• 25 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2021.127870

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We calculate the dynamical critical exponent zzz for 2d and 3d Ising universality classes by means of minimally subtracted five-loop ε\varepsilonε expansion obtained for the A model. This breakthrough turns out to be possible through the successful adaptation of the Sector Decomposition technique to the problems of critical dynamics. The obtained fifth perturbative order accompanied by the use of advanced resummation techniques for asymptotic series allows us to find highly accurate numerical estimates of zzz: for two- and three-dimensional cases we obtain 2.14(2)\boldsymbol{2.14(2)}2.14(2) and 2.0235(8)\boldsymbol{2.0235(8)}2.0235(8) respectively. The numbers found are in good agreement with recent results obtained using different approaches.