Modified percolation theory and its relevance to quantum critical phenomena

Abstract: We present the results of a percolation-like model that has been restricted compared to standard percolation models in the sense that we do not allow finite sized clusters to break up once they have formed. We calculate the critical exponents for this model and derive relationships between these exponents and those of standard percolation models. We argue that this restricted model represents a new universality class that is directly relevant to the critical physics as observed in quantum critical systems, and we describe under what conditions our percolation results can be applied to the observed temperature and field dependencies of the specific heat and susceptibility in such systems.