Percolation mechnisms for long range magnetic order in disordered systems

According to an argument of Harris, a uniform transition in a system with quenched random disorder cannot have a positive specific heat exponent α. We extend this argument to show the existence of a uniform fixed point with a positive α must lead to an inhomogeneous percolative type of phase transition in such a disordered system. We propose a method for calculating the properties of such a transition that is based on a limited application of the uniform renormalization group transformation to the disordered system. Several systems for which this picture might be applicable are discussed.