Temperature-field phase diagram of the two-dimensional dipolar Ising ferromagnet

TL;DR

This study maps the temperature-field phase diagram of a two-dimensional dipolar Ising ferromagnet, revealing differences between mean-field and Monte Carlo predictions of stripe-ordered phases and phase transitions.

Contribution

It provides a detailed comparison of mean-field and Monte Carlo phase diagrams for the dipolar Ising model, highlighting the impact of fluctuations on phase boundaries and stripe patterns.

Findings

Monte Carlo results show reentrant phase transitions not predicted by mean-field theory.

Both methods identify multiple stripe-ordered phases with distinct structures.

Quantitative differences in phase boundaries between MF and MC approaches.

Abstract

We study field-induced phase transitions in the two-dimensional dipolar Ising ferromagnet with a specific ratio between the exchange and dipolar constants, $\delta=1$, which exhibits a stripe-ordered phase with the width of one lattice unit at low temperatures without magnetic field. By using a mean-field (MF) approximation and a Monte Caro (MC) method with the stochastic-cutoff algorithm, which is an $O(N)$ simulation method, we show the temperature-field phase diagrams. In the MC study the orientational order and the structure factor are evaluated. Second-order transition points are determined by a finite-size-scaling analysis and first-order transition points are identified by the analysis of the energy histogram. Although both the MF and MC phase diagrams consist of wide regions of several stripe-ordered phases and narrow regions between them characterized by complicated stripe patterns, they show qualitative and quantitative differences in possible phases and phase boundaries. In the MF phase diagram, three main stripe-ordered phases exhibit a nesting structure, while in the MC phase diagram, two main stripe-ordered phases are located separately, which causes a characteristic field-induced reentrant transition of the orientational order.