Dilatometric Study of LiHoF$_{4}$ In a Transverse Magnetic Field*

Theoretical and experimental work have not presented a consistent picture of the phase diagram of the nearly ideal Ising ferromagnet LiHoF$_{4}$ in a transverse magnetic field. Using a capacitive dilatometer, we have investigated the thermal expansion and magnetostriction of LiHoF$_{4}$ in magnetic fields applied perpendicular to the Ising direction. Critical points for the ferromagnetic phase transition have been determined at low fields close to the classical phase transition. Excellent agreement has been found with existing experimental data suggesting that, in this regime, the current theoretical calculations have not entirely captured the physics of this interesting model system.