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

TL;DR

This paper investigates the dynamic critical behavior of isotropic Heisenberg ferromagnets with free surfaces using field theory and simulations, deriving boundary conditions, renormalization schemes, and confirming predictions with simulation data.

Contribution

It develops a semi-infinite stochastic model J, identifies boundary conditions, and applies renormalization group techniques to analyze surface critical dynamics, supported by simulation results.

Findings

Derived boundary conditions for surface critical dynamics.

Established scaling relations between static and dynamic surface exponents.

Confirmed theoretical predictions with computer simulation data.

Abstract

The dynamic critical behavior of isotropic Heisenberg ferromagnets with a planar free surface is investigated by means of field-theoretic renormalization group techniques and high-precision computer simulations. An appropriate semi-infinite extension of the stochastic model J is constructed. The relevant boundary terms of the action of the associated dynamic field theory are identified, the implied boundary conditions are derived, and the renormalization of the model in $d<6$ bulk dimensions is clarified. Two distinct renormalization schemes are utilized. The first is a massless one based on minimal subtraction of dimensional poles and the dimensionality expansion about $d=6$. To overcome its problems in going below $d=4$ dimensions, a massive one for fixed dimensions $d\le 4$ is constructed. The resulting renormalization group (or Callan Symanzik) equations are exploited to obtain the scaling forms of surface quantities like the dynamic structure factor. In conjunction with boundary operator expansions scaling relations follow that relate the critical indices of the dynamic and static infrared singularities of surface quantities to familiar \emph{static} bulk and surface exponents. To test the predicted scaling forms and scaling-law expressions for the critical exponents involved, accurate computer-simulation data are presented for the dynamic surface structure factor. These are in conformity with our predictions.