We show that mean field theory for the dipole compled Ising model for the specific lattice ofLiHoF4predicts a ferromagnetic critical temperatureTc=2.29&hthinsp;K,which is about 50&percent; above the experimental valueTc=1.53&hthinsp;K.The inclusion of antiferromagnetic exchange interactions lowers the mean fieldTc.We show however that to reach the experimental value, the antiferromagnetic interactions would need to have a strength greater than the ferromagnetic interactions. Hence it can be concluded that mean field theory is not well suited for predicting the correct ordering ofLiHoF4.Including thermal fluctuations we resolve the discrepancy and predict from Monte Carlo simulations that a pair of parallel nearest neighbor Ho-ions have an antiferromagnetic exchange energyE/kB=(0.14±0.01)&hthinsp;K.This is consistent with ferromagnetic ordering. The Monte Carlo results also clearly show that needle-shaped domains form in this system, the extended direction being along the crystalc-axis. ©2000 American Institute of Physics.