Monte Carlo Study of the Phase Transition of the $XY$ Model on a Diamond Lattice

We study the phase transition of the classical $XY$ model on a diamond lattice by Monte Carlo simulations using the Wolff cluster algorithm. Finite-size scaling (FSS) analysis of the Binder cumulant and the second-moment correlation length ratio ${\xi }_{2\mathrm{n}\mathrm{d}}\mathrm{/}L$ yields $T_c=1.30036(1)$ and $\nu =0.671(6)$. Data collapse of both quantities confirms the three-dimensional $XY$ universality class.