Eliminating leading and subleading corrections to scaling in the three-dimensional XY universality class

We study the $(q+1)$-state clock model on the simple cubic lattice by using Monte Carlo simulations. In addition to the nearest neighbor coupling we consider a next-to-next-to-nearest neighbor coupling. For a certain range of the parameters, the phase transition of the model shares the XY universality class. Leading corrections to scaling are studied by using finite size scaling of dimensionless quantities, such as the Binder cumulant $U_4$. The spatial unisotropy, which causes subleading corrections, is studied by computing the exponential correlation length $\xi_{exp}$ in the high temperature phase for different directions. In the case of the $q$-state clock model it turns out that by tuning the ratio of the two coupling constants, we can eliminate either leading or subleading corrections to scaling. These points on the critical line are close to each other. Hence in the improved model, where leading corrections to scaling vanish, also subleading corrections are small. By using a finite size scaling analysis of our high statistics data we obtain $\eta=0.03816(2)$ and $y_t =1/\nu=1.48872(5)$ as estimates of the critical exponents.