A Monte Carlo study of the three-dimensional XY universality class:Universal amplitude ratios

We simulate lattice models in the three-dimensional XY universality class in the low and the high temperature phase. This allows us to compute a number of universal amplitude ratios with unprecedented precision: R_{\Upsilon}=0.411(2), R_B=2.83(1), R_{\xi}^+=0.3562(10) and R_{\xi}^-=0.850(5). These results can be compared with those obtained from other theoretical methods, such as field theoretic methods or the high temperature series expansion and also with experimental results for the lambda-transition of $^4$He. In addition to the XY model, we study the three-dimensional two-component $\phi^4$ model on the simple cubic lattice. The parameter of the $\phi^4$ model is chosen such that leading corrections to scaling are small.