  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.
