# A Monte Carlo study of the three-dimensional XY universality class:Universal amplitude ratios - Condensed Matter > Statistical Mechanics

Abstract: We simulate lattice models in the three-dimensional XY universality class inthe low and the high temperature phase. This allows us to compute a number ofuniversal amplitude ratios with unprecedented precision: R {\Upsilon}=0.4112,R B=2.831, R {\xi}^+=0.356210 and R {\xi}^-=0.8505. These results can becompared with those obtained from other theoretical methods, such as fieldtheoretic methods or the high temperature series expansion and also withexperimental results for the lambda-transition of $^4$He. In addition to the XYmodel, we study the three-dimensional two-component $\phi^4$ model on thesimple cubic lattice. The parameter of the $\phi^4$ model is chosen such thatleading corrections to scaling are small.

Author: Martin Hasenbusch

Source: https://arxiv.org/