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We investigate the critical parameters of an order-disorder quantum phasetransitions in the spin-1/2 $J-J'$ Heisenberg and XY antiferromagnets on squarelattice. Basing on the excitation gaps calculated by exact diagonalizationtechnique for systems up to 32 spins and finite-size scaling analysis weestimate the critical couplings and exponents of the correlation length forboth models. Our analysis confirms the universal critical behavior of thesequantum phase transitions: They belong to 3D O(3) and 3D O(2) universalityclasses, respectively.Comment: 7 pages, 3 figure

Quantum phase transitions in theJ-J' Heisenberg andXYspin-½ antiferromagnets on a square lattice: finite-size scaling analysis