Journal of Statistical Physics, Vol. 29, No. 3, 1982, p. 427-432.
A one-dimensional quantum Hamiltonian which is equivalent to the two-dimensional axial next-nearest-neighbor Ising (ANNNI) model is studied through the derivation and analysis of weak- and strong-coupling perturbation expansions. The phase diagram is constructed and the nature of the phase transitions discussed. In particular, we conclude (i) that there is no Lifshitz point on the ferromagnetic/paramagnetic phase boundary, (ii) there appears to be a Lifshitz point on the antiphase/paramagnetic phase, (iii) above the antiphase Lifshitz point the single transition from paramagnetism to the antiphase is probably continuous and marked by algebraic singularities, (iv) below the antiphase Lifshitz point the transition from paramagnetism to the antiphase is via two transitions, the upper of which is probably of the Kosterlitz/Thouless type, (v) the intermediate phase is presumably incommensurate although the perturbation methods do not directly probe this question.