Surface critical behaviour near the uniaxial Lifshitz point of the axial next-nearest-neighbour Ising model

The semi-infinite axial next-nearest-neighbour Ising (ANNNI) model in the disordered phase is treated within a molecular-field approximation, and the singularities of various response functions characterizing the critical behaviour at the surface are obtained. In previous work (Binder K and Frisch H L 1999 Eur. Phys. J. B 10 71) the axis where a nearest-neighbour ferromagnetic (J 1 ) and next-nearest-neighbour antiferromagnetic (J 2 ) exchange compete was chosen perpendicular to the surface plane. In the present work we consider an orientation of this axis parallel to the surface, allowing also for different values of these exchange interactions (j 1 ,j 2 ) in the surface plane. We derive t…