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Using Monte Carlo simulations we confirm that the rare-earth compound LiHoF4is a very good realization of a dipolar Ising model. With only one freeparameter our calculations for the magnetization, specific heat and inversesusceptibility match experimental data at a quantitative level in the singleKelvin temperature range, including the ferromagnetic transition at 1.53 K.Using parallel tempering methods and reaching system sizes up to 32000 dipoleswith periodic boundary conditions we are able to give strong direct evidence ofthe logarithmic corrections predicted in renormalization group theory. Due tothe long range and angular dependence of the dipolar model sample shape anddomains play a crucial role in the ordered state. We go beyond Griffiths'stheorem and consider surface corrections arising in finite macroscopic samplesleading to a theory of magnetic domains. We predict that the ground-statedomain structure for cylinders with a demagnetization factor N>0 consists ofthin parallel sheets of opposite magnetization, with a width depending on thedemagnetization factor.

The ferromagnetic transition and domain structure in LiHoF4