Computation of the dynamic critical exponent of the three-dimensional Heisenberg model

Abstract

Working in and out of equilibrium and using state-of-the-art techniques we have computed the dynamic critical exponent of the three dimensional Heisenberg model. By computing the integrated autocorrelation time at equilibrium, for lattice sizes $L\le 64$, we have obtained $z=2.033(5)$. In the out of equilibrium regime we have run very large lattices ($L\le 250$) obtaining $z=2.04(2)$ from the growth of the correlation length. We compare our values with that previously computed at equilibrium with relatively small lattices ($L\le 24$), with that provided by means a three-loops calculation using perturbation theory and with experiments. Finally we have checked previous estimates of the static critical exponents, $\eta$ and $\nu$, in the out of equilibrium regime.

10 pages (two columns) and 12 figures. We have extended the paper to cover the equilibrium dynamics of the model

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• Model A of critical dynamics: 5-loop $\epsilon$ expansion study
• Spin-glass dynamics in the presence of a magnetic field: exploration of microscopic properties
• Nonextensive statistical field theory
• Rigorous lower bound on dynamical exponents in gapless frustration-free systems
• Equilibrium and out-of-equilibrium critical dynamics of the three-dimensional Heisenberg model with random cubic anisotropy