The rare-earth material ${\mathrm{LiHoF}}_4$ is believed to be an experimental realization of the celebrated (dipolar) Ising model and, upon the inclusion of a transverse field $B_x$, an archetypal quantum Ising model. Moreover, by substituting the magnetic Ho ions by nonmagnetic Y ions, disorder can be introduced into the system, giving rise to a dipolar disordered magnet and at high disorders to a spin glass. Indeed, this material has been scrutinized experimentally, numerically, and theoretically over many decades with the aim of understanding various collective magnetic phenomena. One of the to-date open questions is the discrepancy between the experimental and theoretical $B_x-T$ phase diagram at low fields and high temperatures. Here we propose a mechanism, backed by numerical results, that highlights the importance of quantum fluctuations induced by the off-diagonal dipolar terms, in determining the critical temperature of anisotropic dipolar magnets in the presence and in the absence of a transverse field. We thus show that the description as a simple Ising system is insufficient to quantitatively describe the full phase diagram of ${\mathrm{LiHoF}}_4$, for the pure as well as for the dilute system.

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• Dipolar interaction
• Magnetic phase transitions
• Magnetism
• Phase diagrams
• Second order phase transitions
• Transition temperature
• Ising model