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 J(1), J(2), with each spin belonging to one J(2)-coupled dimer. A transition from a Neel to disordered ground state occurs at a critical value of g=J(2)/J(1). 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 is an element of[1/2,1]. This unusual behavior is attributed to an effective free-moment density similar to T1-alpha. The susceptibility of the bilayer is not divergent but exhibits remarkably robust quantum-critical scaling.