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

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.

21 pages, 8 figures

References in corpus (6)

• Ising models with long-range dipolar and short-range ferromagnetic interactions
• Ising nematic phase in ultra-thin magnetic films: a Monte Carlo study
• Phase diagram of an Ising model for ultrathin magnetic films
• Striped phases in two dimensional dipole systems
• Interplay between coarsening and nucleation in an Ising model with dipolar interactions
• On the absence of ferromagnetism in typical 2D ferromagnets

Cited by in corpus (6)

• Multicanonical entropy like-solution of statistical temperature weighted histogram analysis method (ST-WHAM)
• Stripe-tetragonal phase transition in the 2D Ising model with dipole interactions: Partition-function zeros approach
• Phase diagram of the two-dimensional dipolar Heisenberg model with the Dzyaloshinskii-Moriya interaction and the Ising anisotropy
• Anisotropy-temperature phase diagram for the two-dimensional dipolar Heisenberg model with and without magnetic field
• Temperature-field phase diagram of the two-dimensional dipolar Ising ferromagnet
• Phase diagram of the dipolar Ising ferromagnet on a kagome lattice