Critical 1- and 2-point spin correlations for the O(2) model in 3d bounded domains

A bstract We study the critical properties of 3 d O (2) universality class in bounded domains through Monte Carlo simulations clock model. use an improved version latter, chosen to minimize finite-size corrections at criticality, with 8 orientations spins and presence vacancies. The domain for is slab configuration fixed boundaries. obtain universal magnetization profile two-point correlations, which favorably compare predictions geometry approach based on Yamabe equation. main result that once dimensionful contributions are factored out profile, shown depend only distance between points computed using a metric found solving corresponding fractional quantitative comparison results Ising model criticality discussed. Moreover, from profiles exponent η extracted be reasonable agreement up-to-date results.