Hidden zero-temperature bicritical point in the two-dimensional anisotropic Heisenberg model: Monte Carlo simulations and proper finite-size scaling

Abstract

By considering the appropriate finite-size effect, we explain the connection between Monte Carlo simulations of two-dimensional anisotropic Heisenberg antiferromagnet in a field and the early renormalization group calculation for the bicritical point in $2+ε$ dimensions. We found that the long length scale physics of the Monte Carlo simulations is indeed captured by the anisotropic nonlinear $σ$ model. Our Monte Carlo data and analysis confirm that the bicritical point in two dimensions is Heisenberg-like and occurs at T=0, therefore the uncertainty in the phase diagram of this model is removed.