  Spin ice is a paradigmatic frustrated system famous for the emergence of
magnetic monopoles and a large magnetic entropy at low temperatures. It
exhibits unusual behavior in the presence of an external magnetic field as a
result of the competition between the spin ice entropy and the Zeeman energy.
Studies of this have generally focused on fields applied along high symmetry
directions: [111], [001], and [110]. Here we consider a model of spin ice with
external field in an arbitrary direction. We find that the Kasteleyn transition
known for $[001]$ fields, appears also for general field directions and
calculate the associated Kasteleyn temperature $T_K$ as a function of field
direction. $T_K$ is found to vanish, with a logarithmic dependence on field
angle, approaching certain lines of special field directions. We further
investigate the thermodynamic properties of spin ice for $T>T_K$, using a
Husimi cactus approximation. As the system is cooled towards $T_K$ a large
magnetic torque appears, tending to align the $[001]$ crystal axis with the
external field. The model also exhibits a rotational magnetocaloric effect:
significant temperature changes can be obtained by adabiatically rotating the
crystal relative to a fixed field.
