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

TL;DR

This paper introduces a systematic Monte Carlo simulation method to study microphase behaviors in lattice models, successfully locating phase boundaries and analyzing critical transitions in the ANNNI and Ising-Coulomb models.

Contribution

The paper presents a novel thermodynamic integration approach for accurately determining phase boundaries in microphase-forming systems.

Findings

Confirmed XY universality of the paramagnetic-modulated transition in ANNNI

Located phase boundaries unambiguously using free energy calculations

Found minimal role of interfacial roughening in layered regimes

Abstract

The equilibrium phase behavior of microphase-forming systems is notoriously difficult to obtain because of the extended metastability of their modulated phases. In this paper we present a systematic simulation methodology for studying layered microphases and apply the approach to two prototypical lattice-based systems: the three-dimensional axial next-nearest-neighbor Ising (ANNNI) and Ising-Coulomb (IC) models. The method involves thermodynamically integrating along a reversible path established between a reference system of free spins under an ordering field and the system of interest. The resulting free energy calculations unambiguously locate the phase boundaries. The simple phases are not observed to play a particularly significant role in the devil's flowers. With the help of generalized order parameters, the paramagnetic-modulated critical transition of the ANNNI model is also studied. We confirm the XY universality of the paramagnetic-modulated transition and its isotropic nature. Interfacial roughening is found to play at most a small role in the ANNNI layered regime.