Critical phenomena in disordered systems: a renormalization-group approach

A renormalization-group method is developed to study critical phenomena in a disordered system. The method bases its considerations on a generalized probability distribution which incorporates both thermodynamic and configurational averaging. Special attention is paid to the higher-order critical phenomena that occur at the percolation limit. A crossover scaling theory describes this region. The equation of the critical line is obtained for the Ising model