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

A. Kudlis; D. A. Evdokimov; D. V. Zakharov; E. V. Ivanova; L. Ts. Adzhemyan; M. Hnati\v{c}; M. V. Kompaniets

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

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arxiv 2111.04719 v2 pith:34YI6CZJ submitted 2021-11-08 cond-mat.stat-mech

L. Ts. Adzhemyan , D. A. Evdokimov , M. Hnatič , E. V. Ivanova , M. V. Kompaniets , A. Kudlis , D. V. Zakharov This is my paper · ORCID

classification cond-mat.stat-mech

keywords criticalobtainedboldsymboldynamicexpansionexponentfive-loopising

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abstract

We calculate the dynamic critical exponent $z$ for 2d and 3d Ising universality classes by means of minimally subtracted five-loop $\varepsilon$ expansion obtained for the one-component model A. 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 $z$: for two- and three-dimensional cases we obtain $\boldsymbol{2.14(2)}$ and $\boldsymbol{2.0235(8)}$ respectively. The numbers found are in good agreement with recent results obtained using different approaches.

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