Surface scaling behavior of isotropic Heisenberg systems: Critical exponents, structure factor, and profiles

The surface scaling behavior of classical isotropic Heisenberg magnets is investigated by Monte Carlo methods in d=3 dimensions for various values of the surface-to-bulk coupling ratio J(1)/J. For J(1)/J less than or equal to 1.0, critical behavior according to the ordinary surface universality class is found. Estimates for magnetic surface exponents are presented and compared to older estimates and their theoretical counterparts. For J(1)/J greater than or equal to 2.0, scaling is still valid with effective exponents which depend on J(1)/J. The surface structure factor S-1(p,L) is investigated at bulk criticality as a function of the momentum transfer p parallel to the surface and the system size L. For J(1)/J less than or equal to 1.0 and J(1)/J greater than or equal to 2.0 the full p dependence of S-1(p,L) can be captured by generalized shape functions to a remarkable accuracy. Profiles of the magnetization and the energy density also confirm scaling, where for J(1)/J less than or equal to 1.0 the ordinary surface universality class is recovered and for J(1)/J greater than or equal to 2.0, scaling with J(1)/J dependent exponents is found. For J(1)/J=1.5 the system displays a striking crossover behavior from spurious long-range surface order to the ordinary surface universality class. For J(1)/J greater than or equal to 2.0 the effective scaling laws must be interpreted as nonasymptotic and the value J(1)/J=1.5 marks a crossover regime, in which the crossover from the nonasymptotic to the asymptotic (ordinary) surface scaling behavior can be resolved within numerically attainable system sizes.