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 $\ensuremath{\sigma}$ 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.
Extensive Monte Carlo simulations are used to locate the bicritical point of the ferromagnetic anisotropic Heisenberg model on a simple cubic lattice in the presence of a crystal field. In order to achieve this goal, we employ a hybrid algorithm comprising Metropolis and Wolff algorithms along with field mixing. Multiple histogram techniques have also been used to obtain the probability distribution function of the conjugate extensive variables of interest. In conjunction with finite-size scaling analysis we computed the fourth-order cumulant of the order parameter along the first-order line and the corresponding bicritical point has been located from the crossings of the cumulants.