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Using Monte Carlo techniques, the surface critical behaviour ofthree-dimensional semi-infinite ANNNI models with different surfaceorientations with respect to the axis of competing interactions isinvestigated. Special attention is thereby paid to the surface criticality atthe bulk uniaxial Lifshitz point encountered in this model. The presented MonteCarlo results show that the mean-field description of semi-infinite ANNNImodels is qualitatively correct. Lifshitz point surface critical exponents atthe ordinary transition are found to depend on the surface orientation. At thespecial transition point, however, no clear dependency of the criticalexponents on the surface orientation is revealed. The values of the surfacecritical exponents presented in this study are the first estimates availablebeyond mean-field theory.Comment: 10 pages, 7 figures include

Surface critical exponents at a uniaxial Lifshitz point