Some features of the phase diagram of the two-dimensional ANNNI model have long been debated. The extended structural correlations and relaxation times associated with its Kosterlitz-Thouless (KT) phase indeed result in analytical and numerical treatments making contradictory predictions. Here we introduce a numerical transfer matrix approach that bypasses these problems and thus clears up various ambiguities. In particular we confirm the transition temperatures and the order of the transition to the floating incommensurate phase. Our approach motivates considering transfer matrices for solving long-standing problems in related models.
