Quantum criticality and percolation in dimer-diluted two-dimensional antiferromagnets

The S = 1/2 Heisenberg model is considered on bilayer and single-layer square lattices with couplings J1, J2, with each spin belonging to one J2-coupled dimer. A transition from a Néel to disordered ground state occurs at a critical value of g = J2/J1. The systems are here studied at their dimer-dilution percolation points p*. The multicritical point (g*,p*) previously found for the bilayer is not reproduced for the single layer. Instead, there is a line of critical points (g < g*, p*) with continuously varying exponents. The uniform magnetic susceptibility diverges as T(-alpha) with alpha element of 1/2,1]. This unusual behavior is attributed to an effective free-moment density approximately T(1-alpha). The susceptibility of the bilayer is not divergent but exhibits remarkably robust quantum-critical scaling.