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

Abstract

We calculate the dynamic critical exponent $z$ for 2d and 3d Ising universality classes by means of minimally subtracted five-loop $\epsilon$ 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.

References in corpus (4)

• Non-perturbative Approach to Critical Dynamics
• Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark
• Critical slowing down near the multiferroic phase transition in MnWO${}_4$
• Calculations of the dynamical critical exponent using the asymptotic series summation method