  The phase diagram of the two-dimensional ANNNI model has long been
theoretically debated. Extremely long structural correlations and relaxation
times further result in numerical simulations making contradictory predictions.
Here, we introduce a numerical transfer matrix treatment that bypasses these
problems, and thus overcome various ambiguities in the phase diagram. In
particular, we confirm the transition temperatures and clarify the order of the
transition to the floating incommensurate phase. Our approach motivates
considering transfer matrices for resolving long-standing problems in related
statistical physics models.
