Calculation of universal amplitude ratios in three-loop order Original Research Article

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 ø4 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 dC+/C− = 4.72(17).