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

Abstract

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 <= 1.0 critical behavior according to the ordinary surface universality class is found. New estimates for magnetic surface exponents are presented and compared to older estimates and their theoretical counterparts. For J_1/J >= 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 function of the momentum transfer p parallel to the surface and the system size L. For J_1/J <= 1.0 and J_1/J >= 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 <= 1.0 the ordinary surface universality class is recovered and for J_1/J >= 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 >= 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.