Finite-size scaling of two-dimensional axial next-nearest-neighbor Ising models

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Abstract
A finite-size-scaling analysis is applied to two axial next-nearest-neighbor Ising (ANNNI) models. By using the scaling behavior of both the correlation length and the modulation wave vector we are able to clearly identify and distinguish between the ordered commensurate phases, the lock-in fluid phases, and in particular, the two types of incommensurate (floating) phases occurring in the models. As expected, the brickwork ANNNI model does not have a floating-solid phase, but instead has a q=(1/4) lock-in fluid phase above its 〈2〉 phase. On the basis of our results, we conclude that, in contrast to a recent suggestion, transfer-matrix methods can be a powerful tool in the study of two-dimensional models which exhibit incommensurate phases.