Solution of the random field XY magnet on a fully connected graph

We use large deviation theory to obtain the free energy of the XY model on a fully connected graph on each site of which there is a randomly oriented field of magnitude $h$. The phase diagram is obtained for two symmetric distributions of the random orientations: (a) a uniform distribution and (b) a distribution with cubic symmetry. In both cases, the ordered state reflects the symmetry of the underlying disorder distribution. The phase boundary has a multicritical point which separates a locus of continuous transitions (for small values of $h$) from a locus of first order transitions (for large $h$). The free energy is a function of a single variable in case (a) and a function of two variables in case (b), leading to different characters of the multicritical points in the two cases.

Experimental realization of a 3D random hopping model

Scientific advance is often driven by identifying conceptually simple models underlying complex phenomena. This process commonly ignores imperfections which, however, might give rise to non-trivial collective behavior. For example, already a small amount of disorder can dramatically change the transport properties of a system compared to the underlying simple model. While systems with disordered potentials were already studied in detail, experimental investigations on systems with disordered hopping are still in its infancy. To this end, we experimentally study a dipole–dipole-interacting three-dimensional Rydberg system and map it onto a simple XY model with random couplings by spectroscopic evidence. We discuss the localization–delocalization crossover emerging in the model and present experimental signatures of it. Our results demonstrate that Rydberg systems are a useful platform to study random hopping models with the ability to access the microscopic degrees of freedom. This will allow to study transport processes and localization phenomena in random hopping models with a high level of control.

Uniformly Frustrated XY Model: Strengthening of the Vortex Lattice by Intrinsic Disorder

In superconducting films, the role of intrinsic disorder is typically to compete with superconductivity by fragmenting the global phase coherence and lowering the superfluid density. Nonetheless, when a transverse magnetic field is applied to the system and an Abrikosov vortex lattice form, the presence of disorder can actually strengthen the superconducting state against thermal fluctuations. By means of Monte Carlo simulations on the uniformly frustrated XY model in two dimensions, we show that while for weak pinning the superconducting critical temperature Tc increases with the applied field H, for strong enough pinning, the experimental decreasing dependence between Tc and H is recovered with a resulting more robust vortex lattice.

Conditional generative models for sampling and phase transition indication in spin systems

In this work, we study generative adversarial networks (GANs) as a tool to learn the distribution of spin configurations and to generate samples, conditioned on external tuning parameters or other quantities associated with individual configurations. For concreteness, we focus on two examples of conditional variables---the temperature of the system and the energy of the samples. We show that temperature-conditioned models can not only be used to generate samples across thermal phase transitions, but also be employed as unsupervised indicators of transitions. To this end, we introduce a GAN-fidelity measure that captures the model’s susceptibility to external changes of parameters. The proposed energy-conditioned models are integrated with Monte Carlo simulations to perform over-relaxation steps, which break the Markov chain and reduce auto-correlations. We propose ways of efficiently representing the physical states in our network architectures, e.g., by exploiting symmetries, and to minimize the correlations between generated samples. A detailed evaluation, using the two-dimensional XY model as an example, shows that these incorporations bring in considerable improvements over standard machine-learning approaches. We further study the performance of our architectures when no training data is provided near the critical region.