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We study the three-dimensional Kasteleyn transition in both nearestneighbours and dipolar spin ice models using an algorithm that conserves thenumber of excitations. We first limit the interactions range to nearestneighbours to test the method in the presence of a field applied along $[100]$,and then focus on the dipolar spin ice model. The effect of dipolarinteractions, which is known to be greatly self screened at zero field, isparticularly strong near full polarization. It shifts the Kasteleyn transitionto lower temperatures, which decreases $\approx 0.4 K$ for the parameterscorresponding to the best known spin ice materials, $Dy_2Ti_2O_7$ and$Ho_2Ti_2O_7$. This shift implies effective dipolar fields as big as $0.05$tesla opposing the applied field, and thus favoring the creation of "strings"of reversed spins. We compare the reduction in the transition temperature withresults in previous experiments, and study the phenomenon quantitatively usinga simple molecular field approach. Finally, we relate the presence of theeffective residual field to the appearance of string-ordered phases at lowfields and temperatures, and we check numerically that for fields applied along$[100]$ there are only three different stable phases at zero temperature.

The 3D Kasteleyn transition in dipolar spin ice: a numerical study with the Conserved Monopoles Algorithm