Journal of Statistical Physics, Vol. 52, No. 1/2, 1988. p. 113-142.
We introduce an equivalence relation on the family of ground states and generalize the Peierls and PJrogov-Sinai theory of phase transitions to systems with residual entropy. The idea consists in the replacement of the periodic ground states by equivalence classes together with an entropy factor. We apply these results to discuss the phase diagrams of diluted spin-l/2 systems.