The dynamic critical exponent $z$ of the three-dimensional Ising universality class: Monte Carlo simulations of the improved Blume-Capel model

Abstract

We study purely dissipative relaxational dynamics in the three-dimensional Ising universality class. To this end, we simulate the improved Blume-Capel model on the simple cubic lattice by using local algorithms. We perform a finite size scaling analysis of the integrated autocorrelation time of the magnetic susceptibility in equilibrium at the critical point. We obtain $z=2.0245(15)$ for the dynamic critical exponent. As a complement, fully magnetized configurations are suddenly quenched to the critical temperature, giving consistent results for the dynamic critical exponent. Furthermore, our estimate of $z$ is fully consistent with recent field theoretic results.

37 pages, 6 figures; largely extended compared with previous version, additional simulations

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