Cavity-fields approach to quadrupolar glass

The cavity-fields approach recently proposed and used in spin-glass theory is extended to study the infinite-range quadrupolar-glass model and the three-state Potts spin-glass model. This approach, which avoids the replica method, relies on well-known mathematical grounds and deals with obvious physical quantities; the Thouless-Anderson-Palmer equations are obtained for both models. The results are in agreement with the previous calculations based on the replica method.