Percolation and Quantum Criticality: a New Universality Class

We present the results of computer simulations on a class of percolation systems that form a new universality class. We show the results for the critical exponents for this new class, based on simulations of two- and three-dimensional lattices consisting of half a billion sites, and discuss the ensuing modified scaling laws.
This new percolation system, dubbed Protected Percolation, differs from standard site percolation in that once a cluster breaks off the percolating cluster, its sites become protected and cannot be removed; thus, only sites from the lattice spanning cluster can be removed. This restriction closely mimics the situation in chemically doped quantum critical systems where isolated magnetic clusters are protected from (further) Kondo screening. Initial results indicate that Protected Percolation violates the Harris Criterion, which leads to a natural explanation as to why universal critical exponents for quantum phase transitions have been elusive.