Calculation of Universal Amplitude Ratios in three-loop order

TL;DR

This paper calculates universal amplitude ratios for three-dimensional Ising systems at three-loop order using renormalized perturbation theory, providing precise numerical estimates for these universal quantities.

Contribution

It presents the first three-loop order calculation of universal amplitude ratios in scalar ^4 theory for the 3D Ising universality class.

Findings

Calculated amplitude ratios: f+/f- = 2.013(28), C+/C- = 4.72(17)

Demonstrated the use of fixed point coupling constants in three-loop perturbation theory

Enhanced precision in universal amplitude ratio estimates for 3D Ising systems.

Abstract

For the universality class of three-dimensional Ising systems the ratio of the high- and low-temperature amplitudes for the correlation length and for the susceptibility are universal quantities. They can be calculated by renormalized perturbation theory for scalar $\phi^4$ theory in fixed dimensions $D=3$ in the symmetric phase and in the phase of broken symmetry. In this article the amplitude ratios are calculated in the three-loop approximation. Using the fixed point values of the coupling constants we obtain $f_+/f_-=2.013(28)$ and $C_+/C_-=4.72(17)$.