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

TL;DR

This paper computes highly accurate dynamic critical exponents for 2d and 3d Ising models using a five-loop epsilon expansion and advanced resummation techniques, confirming recent findings.

Contribution

It introduces the adaptation of Sector Decomposition to critical dynamics and achieves the first five-loop epsilon expansion for the model A universality class.

Findings

Estimated z for 2d Ising: 2.14(2)

Estimated z for 3d Ising: 2.0235(8)

Results agree with recent alternative approaches

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.