English

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

Statistical Mechanics 2022-01-05 v2

Abstract

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

Keywords

Cite

@article{arxiv.2111.04719,
  title  = {The dynamic critical exponent $z$ for 2d and 3d Ising models from five-loop $\epsilon$ expansion},
  author = {L. Ts. Adzhemyan and D. A. Evdokimov and M. Hnatič and E. V. Ivanova and M. V. Kompaniets and A. Kudlis and D. V. Zakharov},
  journal= {arXiv preprint arXiv:2111.04719},
  year   = {2022}
}
R2 v1 2026-06-24T07:31:10.349Z