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The equilibrium phase behavior of microphase-forming systems is notoriouslydifficult to obtain because of the extended metastability of their modulatedphases. In this paper we present a systematic simulation methodology forstudying layered microphases and apply the approach to two prototypicallattice-based systems: the three-dimensional axial next-nearest-neighbor Ising(ANNNI) and Ising-Coulomb (IC) models. The method involves thermodynamicallyintegrating along a reversible path established between a reference system offree spins under an ordering field and the system of interest. The resultingfree energy calculations unambiguously locate the phase boundaries. The simplephases are not observed to play a particularly significant role in the devil'sflowers. With the help of generalized order parameters, theparamagnetic-modulated critical transition of the ANNNI model is also studied.We confirm the XY universality of the paramagnetic-modulated transition and itsisotropic nature. Interfacial roughening is found to play at most a small rolein the ANNNI layered regime.

A Monte Carlo Approach for Studying Microphases Applied to the Axial Next-Nearest-Neighbor Ising and the Ising-Coulomb Models