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

TL;DR

This study uses Monte Carlo simulations of 3D XY models to precisely calculate universal amplitude ratios, providing benchmarks for theoretical and experimental comparisons in critical phenomena.

Contribution

It presents highly accurate Monte Carlo estimates of universal amplitude ratios in the 3D XY universality class, including analysis of the $ ext{phi}^4$ model with minimized corrections to scaling.

Findings

Universal amplitude ratios with unprecedented precision: R_Υ=0.411(2), R_B=2.83(1), R_ξ^+=0.3562(10), R_ξ^-=0.850(5)

Results agree with field theory, series expansion, and helium experiments

Studied $ ext{phi}^4$ model to reduce scaling corrections

Abstract

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.