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The dynamic critical behavior of isotropic Heisenberg ferromagnets with aplanar free surface is investigated by means of field-theoretic renormalizationgroup techniques and high-precision computer simulations. An appropriatesemi-infinite extension of the stochastic model J is constructed. The relevantboundary terms of the action of the associated dynamic field theory areidentified, the implied boundary conditions are derived, and therenormalization of the model in $d<6$ bulk dimensions is clarified. Twodistinct renormalization schemes are utilized. The first is a massless onebased on minimal subtraction of dimensional poles and the dimensionalityexpansion about $d=6$. To overcome its problems in going below $d=4$dimensions, a massive one for fixed dimensions $d\le 4$ is constructed. Theresulting renormalization group (or Callan Symanzik) equations are exploited toobtain the scaling forms of surface quantities like the dynamic structurefactor. In conjunction with boundary operator expansions scaling relationsfollow that relate the critical indices of the dynamic and static infraredsingularities of surface quantities to familiar \emph{static} bulk and surfaceexponents. To test the predicted scaling forms and scaling-law expressions forthe critical exponents involved, accurate computer-simulation data arepresented for the dynamic surface structure factor. These are in conformitywith our predictions.Comment: Revtex4-file with 4 figures included as eps-files, 21 pages in  print-format, typos corrected, to appear in Phys. Rev. B, July

physical review. b, condensed matter

Dynamic surface critical behavior of isotropic Heisenberg ferromagnets: Boundary conditions, renormalized field theory, and computer simulation results