Phase transitions and autocorrelation times in two-dimensional Ising model with dipole interactions

TL;DR

This study investigates phase transitions and critical slowing down in a 2D Ising model with dipolar interactions, revealing complex phase behavior and autocorrelation properties through Monte Carlo simulations.

Contribution

It provides detailed analysis of phase transitions, critical exponents, and autocorrelation times in the dipolar Ising model, highlighting the impact of long-range interactions.

Findings

Identification of critical temperatures for stripe-nematic and nematic-tetragonal transitions

Calculation of critical exponents and free-energy barriers

Observation of critical slowing down near phase transitions

Abstract

The two-dimensional Ising model with nearest-neighbor ferromagnetic and long-range dipolar interactions exhibits a rich phase diagram. The presence of the dipolar interaction changes the ferromagnetic ground state expected for the pure Ising model to a series of striped phases as a function of the interaction strengths. Monte Carlo simulations and histogram reweighting techniques applied to multiple histograms are performed to identify the critical temperatures for the phase transitions taking place for stripes of width $h=2$ on square lattices. In particular, we aim to study the intermediate nematic phase, which is observed for large lattice sizes only. For these lattice sizes, we calculate the critical temperatures for the striped-nematic and nematic-tetragonal transitions, critical exponents, and the bulk free-energy barrier associated with the coexisting phases. We also evaluate the long-term correlations in our time series near the finite-size critical points by studying the integrated autocorrelation time $\tau$ as a function of the lattice size. This allows us to infer how severe the critical slowing down for this system with long-range interaction and nearby thermodynamic phase transitions is.