Monte Carlo Study of the Axial Next-Nearest-Neighbor Ising Model

TL;DR

This study uses a novel simulation method to accurately determine the phase diagram and critical behavior of the 3D axial next-nearest-neighbor Ising model, revealing the limitations of previous approximation schemes.

Contribution

Develops a thermodynamic integration-based simulation approach to map the phase diagram of the 3D axial next-nearest-neighbor Ising model, overcoming metastability issues.

Findings

Identifies the equilibrium devil's staircase and phase transition characteristics.

Confirms XY universality class of the phase transition.

Highlights limitations of existing approximation methods.

Abstract

The equilibrium phase behavior of microphase-forming substances and models is notoriously difficult to obtain because of the extended metastability of the modulated phases. We develop a simulation method based on thermodynamic integration that avoids this problem and with which we obtain the phase diagram of the canonical three-dimensional axial next-nearest-neighbor Ising model. The equilibrium devil's staircase, magnetization, and susceptibility are obtained. The critical exponents confirm the XY nature of the disorder-modulated phase transition beyond the Lifshitz point. The results identify the limitations of various approximation schemes used to analyze this basic microphase-forming model.