We study magnetic-field-induced three-dimensional ordering transitions in low-dimensional quantum spin liquids, such as weakly coupled, antiferromagnetic spin- $1/2$ Heisenberg dimers and ladders. Using stochastic series expansion quantum Monte Carlo simulations, we obtain the critical scaling exponents which dictate the power-law dependence of the transition temperature on the magnetic field. These are compared with recent experiments on candidate materials and with predictions for the Bose-Einstein condensation of magnons. The critical exponents deviate from isotropic mean-field theory and exhibit different scaling behavior at the lower and upper critical magnetic fields.

• Received 24 May 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.206407