Quadrupolar quantum criticality on a fractal

We study the ground state ordering of quadrupolar ordered S=1 magnets as a function of spin dilution probability p on the triangular lattice. In sharp contrast to the ordering of S=1/2 dipolar Néel magnets on percolating clusters, we find that the quadrupolar magnets are quantum disordered at the percolation threshold, p=p∗. Further we find that long-range quadrupolar order is present for all p<p∗ and vanishes first exactly at p∗. Strong evidence for scaling behavior close to p∗ points to an unusual quantum criticality without fine tuning that arises from an interplay of quantum fluctuations and randomness.