Criticality in coupled quantum spin-chains with competing ladder-like and two-dimensional couplings

Motivated by the geometry of spins in the material CaCu${}_2$O${}_3$, we study a two-layer, spin-half Heisenberg model, with nearest-neighbor exchange couplings J and \alpha*J along the two axes in the plane and a coupling J_\perp perpendicular to the planes. We study these class of models using the Stochastic Series Expansion (SSE) Quantum Monte Carlo simulations at finite temperatures and series expansion methods at T=0. The critical value of the interlayer coupling, J_\perp^c, separating the N{'e}el ordered and disordered ground states, is found to follow very closely a square root dependence on $\alpha$. Both T=0 and finite-temperature properties of the model are presented.