Abstract
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 (J1) and next-nearest-neighbour antiferromagnetic (J2) 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 (j1,j2) in the surface plane. We derive the conditions for the occurrence of a surface transition, where the surface plane (at a temperature where the bulk is still disordered) orders either ferromagnetically or into a modulated structure. At the ordinary transition of the surface we obtain the mean-field values of the surface critical exponents, including the Lifshitz point of the bulk, where L1 = 1/2, L11 = -1/2, L = 0, L = 3. These exponents differ from their counterparts for the case where the axis of competing interactions is oriented perpendicular to the surface, and thus it is shown that for a uniaxial Lifshitz point the surface critical behaviour depends on the surface orientation.
Published Version
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