GPU-Accelerated Monte Carlo Study of the 2D XY Model and the Berezinskii–Kosterlitz–Thouless Transition on Non-Square Lattices

We perform large-scale GPU-accelerated Monte Carlo simulations of the two-dimensional XY model on square, triangular, honeycomb, and kagome lattices with up to 10^9 spins. Using a hybrid local–global update scheme, we compute the helicity modulus, vortex density, and vortex–antivortex correlations. The results confirm the Berezinskii–Kosterlitz–Thouless (BKT) transition and its universal jump criterion. This work provides the first systematic GPU-based study of XY models on non-square lattices, revealing geometry-dependent finite-size effects and performance gains from hybrid updates.