Commensurate-incommensurate phase transitions and wetting in a lattice-gas model with axially competing interactions

The two-dimensional axial next-nearest-neighbor Ising model in an external magnetic field is studied at low temperatures with the use of transfer-matrix techniques. Commensurate-incommensurate phase boundaries are calculated with improved free-fermion approximations which take into account the presence of both light and heavy walls. Special attention is paid to the case when three different periodicities compete. In the incommensurate phases the structure factor shows a multimodulated structure, which is calculated explicitly. Our approach makes possible the analytic determination of the wetting lines in the 2,1 phase which end at a new type of multicritical point. Results are tested by Monte Carlo simulations. © 1985 The American Physical Society.