Five-loop expansion for a universal combination of critical amplitudes of the 3D dilute Ising model

Double expansions of the universal combination Rξ+ of the critical amplitudes of the singular part of the specific heat and of the correlation length in the homogeneous phase of the 3D and 2D dilute Ising models are calculated to the fourth and third order, respectively, in powers of the renormalized coupling constants. The calculation is performed within the framework of renormalized perturbation theory in fixed dimension. Numerical estimates are obtained by the use of Padé–Borel–Leroy approximation. The Rξ+ estimate for the 3D case is comparable in accuracy to the critical exponent values, while for the test case of 2D Ising model it is in accordance with the exact value .