The O( N) Heisenberg model on a three-dimensional lattice is expanded in powers of N −1. The inverse correlation length and the magnetic field as funetions of the coupling constant (temperature) and magnetization are studied in the critical domain. A method to extract analytic expressions for non-universal quantities is developed. It is based on a systematic expansion in powers of the infrared cutoff mass around the continuum approximation. In particular our method is independent of the specific model studied here and can be applied to quite a general class of problems, e.g., Symanzik's improvement program.