Criticality and scaling corrections for two-dimensional Heisenberg models in plaquette patterns with strong and weak couplings

We use the stochastic series expansion quantum Monte Carlo method to study the Heisenberg models on the square lattice with strong and weak couplings in the form of three different plaquette arrangements known as checkerboard models C2×2, C2×4, and C4×4. The a×b here stands for the shape of the plaquette consisting of spins connected by strong couplings. Through detailed analysis of a finite-size scaling study, the critical point of the C2×2 model is improved as gc=0.548524(3) compared with previous studies where g is the ratio of weak and strong couplings in the models. For C2×4 and C4×4 we give gc=0.456978(2) and 0.314451(3). We also study the critical exponents ν and η and the universal property of the Binder ratio to give further evidence that all quantum phase transitions in these three models are in the three-dimensional O(3) universality class. Furthermore, our fitting results show the importance of effective corrections in the scaling study of these models.