Quantum phase transitions in the J-J' Heisenberg and XY spin-1/2 antiferromagnets on a square lattice:: finite-size scaling analysis

We investigate the critical parameters of an order-disorder quantum phase transition in the spin-1/2 J-J ' Heisenberg and XY antiferromagnets on a square lattice. Based on the excitation gaps calculated by the exact diagonalization technique for systems up to 32 spins and finite-size scaling analysis we estimate the critical couplings and exponents of the correlation length for both models. Our analysis confirms the universal critical behaviour of these quantum phase transitions: they belong to 3D O(3) and 3D O(2) universality classes, respectively.