Abstract. We develop an $1/n$ expansion method for the systematic approximation of the solutions of classical spin systems (tri-dimensional vectors) which can describe general spin-spin interactions and phases with complex magnetization pattern. This method is applied to study the phase transitions observed in pyrochlore crystals (e.g. Gd₂Ti₂O₇) and the results have qualitative agreement with the experimental ones.

Key words: Phase transition, antiferromagnetism, spherical model.