Zhang, K; Charbonneau, P, *Monte carlo study of the axial next-nearest-neighbor Ising model.*,
Phys Rev Lett, vol. 104 no. 19
(May, 2010),
pp. 195703 [20866979], [doi] .
**Abstract:**

*The equilibrium phase behavior of microphase-forming systems is notoriously difficult to obtain because of the extended metastability of the modulated phases. We develop a simulation method based on free-energy integration that surmounts this problem and with which we describe the modulated regime of the canonical three-dimensional axial next-nearest-neighbor Ising model. Equilibrium order parameters are obtained and the critical behavior beyond the Lifshitz point is examined. The absence of widely extended bulging modulated phases illustrates the limitations of various approximation schemes used to analyze microphase-forming models.*