Calculation of Universal Amplitude Ratios in three-loop order

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 $ϕ^4$ 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 $C_+/C_-=4.72(17)$.