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

L. Ts Adzhemyan, D. A. Evdokimov, M. Hnatič, E. V. Ivanova, M. V. Kompaniets, A. Kudlis, D. V. Zakharov

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We calculate the dynamical critical exponent z for 2d and 3d Ising universality classes by means of minimally subtracted five-loop ε 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 2.14(2) and 2.0235(8) respectively. The numbers found are in good agreement with recent results obtained using different approaches.

Original languageEnglish
Article number127870
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
StatePublished - 16 Feb 2022

Scopus subject areas

  • Physics and Astronomy(all)


  • Critical dynamic exponent z
  • Critical dynamics
  • Multi-loop calculation
  • Renormalization group
  • ε expansion


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