Two-dimensional dipolar XY magnetism in thermal equilibrium

Motivated by a recent experiment on a square-lattice Rydberg atom array realizing a long-range dipolar XY model [Chen et al., arxiv:2207.12930], we numerically study the model's equilibrium properties. We obtain the phase diagram, critical properties, entropies and site-resolved correlation functions. We consider both ferromagnetic and antiferromagnetic interactions and apply quantum Monte Carlo and the pseudo-Majorana functional renormalization group. Our simulations quantitatively reproduce the experimentally measured spatial decay of correlations with only temperature as a tuning parameter and thus provide a thermometry protocol. Surprisingly, the entropies extracted for both signs of the coupling turn out to be rather high, ~0.7 log 2, calling for an investigation into possibly non-adiabatic heating sources in the experiment.