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 Néel 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 $\alpha \in [1/2,1]$. This unusual behavior is attributed to an effective free-moment density $\sim T^{1-\alpha }$. The susceptibility of the bilayer is not divergent but exhibits remarkably robust quantum-critical scaling.

• Received 7 March 2006

DOI:https://doi.org/10.1103/PhysRevLett.96.207201