From one to two dimensions in quantum spin systems

We study the first derivative of the staggered magnetization squared $dm^\dag(\theta)^2/d\theta$ and the second derivative $d^2e_0(\theta)/d\theta^2$ of the ground state energy per site. The parameter $\theta$ controls the anisotropy between horizontal and vertical couplings in a two-dimensional (2D) spin-1/2 antiferromagnetic Heisenberg model. It is shown, that both derivatives diverge at $\theta=1$, where the anisotropic 2D model reduces to the 1D model.