Protected percolation: a new universality class pertaining to heavily-doped quantum critical systems

Abstract

We present computer simulations on a class of percolative systems that forms a new universality class. We determine the universal critical exponents for this new class from simulations on lattices consisting of up to one billion sites. These new percolative systems differ from standard systems in that once a cluster breaks off the lattice spanning cluster, its sites become protected and cannot be removed. We demonstrate that despite this restriction on the evolution of isolated clusters, the scaling relationships between the critical exponents remain valid. Protected percolation closely mimics the situation in heavily-doped quantum critical systems where isolated magnetic clusters are protected from Kondo screening. We show that protected percolation in three dimensions violates the Harris criterion, explaining why universal exponents for quantum phase transitions have been elusive.