The recent discovery of tunable Dzyaloshinskii-Moriya interactions in layered magnetic materials with perpendicular magnetic anisotropy makes them promising candidates for stabilization and manipulation of skyrmions at elevated temperatures. In this article, we use Monte Carlo simulations to investigate the robustness of skyrmions in these materials against thermal fluctuations and finite-size effects. We find that in confined geometries and at finite temperatures skyrmions are present in a large part of the phase diagram. Moreover, we find that the confined geometry favors the skyrmion over the spiral phase when compared to infinitely large systems. Upon tuning the magnetic field through the skyrmion phase, the system undergoes a cascade of transitions in the magnetic structure through states of different number of skyrmions, elongated and half-skyrmions, and spiral states. We consider how quantum and thermal fluctuations lift the degeneracies that occur at these transitions, and find that states with more skyrmions are typically favored by fluctuations over states with less skyrmions. Finally, we comment on electrical detection of the various phases through the topological and anomalous Hall effects.

The ground states of square-lattice two-dimensional antiferromagnets with anisotropy in an external magnetic field are determined using Monte Carlo simulations and compared to theoretical analysis. We find a phase in between the spin-flop and spiral phase that shows strong similarity to skyrmions in ferromagnetic thin films. We show that this phase arises as a result of the competition between Zeeman and Dzyaloshinskii-Moriya interaction energies of the magnetic system. Moreover, we find that isolated (anti-)skyrmions are stabilized in finite-sized systems, even at higher temperatures. The existence of thermodynamically stable skyrmions in square-lattice antiferromagnets provides an appealing alternative over skyrmions in ferromagnets as data carriers.

We perform a numerical study of the F model with domain-wall boundary conditions. Various exact results are known for this particular case of the six-vertex model, including closed expressions for the partition function for any system size as well as its asymptotics and leading finite-size corrections. To complement this picture we use a full lattice multicluster algorithm to study equilibrium properties of this model for systems of moderate size, up to L = 512. We compare the energy to its exactly known large-L asymptotics. We investigate the model's infinite-order phase transition by means of finite-size scaling for an observable derived from the staggered polarization in order to test the method put forward in our recent joint work with Duine and Barkema. In addition we analyze local properties of the model. Our data are perfectly consistent with analytical expressions for the arctic curves. We investigate the structure inside the temperate region of the lattice, confirming the oscillations in vertex densities that were first observed by Syljuåsen and Zvonarev and recently studied by Lyberg et al. We point out "(anti)ferroelectric" oscillations close to the corresponding frozen regions as well as "higher-order" oscillations forming an intricate pattern with saddle-point-like features.

For systems with infinite-order phase transitions, in which an order parameter smoothly becomes nonzero, a new observable for finite-size scaling analysis is suggested. By construction this new observable has the favourable property of diverging at the critical point. Focussing on the example of the F -model we compare the analysis of this observable with that of another observable, which is also derived from the order parameter but does not diverge, as well as that of the associated susceptibility. We discuss the difficulties that arise in the finite-size scaling analysis of such systems. In particular we show that one may reach incorrect conclusions from large-system size extrapolations of observables that are not known to diverge at the critical point. Our work suggests that one should base finite-size scaling analyses for infinite-order phase transitions only on observables that are guaranteed to diverge.