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Physica A Statistical Mechanics and its Applications

The dynamical critical exponent of the two-, three- and five-dimensional kinetic Ising model

Christian Münkel, Dieter W. Heermann, Joan Adler, Misha Gofman, Dietrich Stauffer

Published Apr 1, 1993• 69 citations
Publisher
DOI
10.1016/0378-4371(93)90490-u

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

L. Ts. Adzhemyan, Daniil A. Evdokimov, Michal Hnatič +4 more

We calculate the dynamical critical exponent $z$ for 2d and 3d Ising universality classes by means of minimally subtracted five-loop $\varepsilon$ expansion obtained for the A model. 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.

•Nov 8, 2021•0 citations
The coherent-anomaly method (CAM) is applied to the kinetic Ising model. Dynamical cluster-mean-field approximations are formulated to obtain a series of the dynamical mean-field critical coefficients. The coherent-anomaly scaling relations are derived on the basis of the scaling form of the generating function in nonequilibrium systems to estimate the exponent Δ of the critical slowing down. The dynamical critical exponent is estimated as Δ⋍2.15(±0.02){\varDelta}{\backsimeq}2.15({\pm}0.02)Δ⋍2.15(±0.02) for the kinetic Ising model on the two-dimensional triangular lattice.
The dynamical critical exponent zzz for 2d and 3d Ising models from five-loop ϵ\epsilonϵ expansion
We calculate the dynamical critical exponent zzz for 2d and 3d Ising universality classes by means of minimally subtracted five-loop ε\varepsilonε expansion obtained for the A model. 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 zzz: for two- and three-dimensional cases we obtain 2.14(2)\boldsymbol{2.14(2)}2.14(2) and 2.0235(8)\boldsymbol{2.0235(8)}2.0235(8) respectively. The numbers found are in good agreement with recent results obtained using different approaches.