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The rare-earth material $\mathrm{LiHoF_4}$ is believed to be an experimentalrealization of the celebrated (dipolar) Ising model, and upon the inclusion ofa transverse field $B_x$, an archetypal quantum Ising model. Moreover, bysubstituting the magnetic Ho ions by non-magnetic Y ions, disorder can beintroduced into the system giving rise to a dipolar disordered magnet and athigh disorders to a spin-glass. Indeed, this material has been scrutinizedexperimentally, numerically and theoretically over many decades with the aim ofunderstanding various collective magnetic phenomena. One of the to-date openquestions 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 quantumfluctuations induced by the off-diagonal dipolar terms, in determining thecritical temperature of anisotropic dipolar magnets in the presence and in theabsence of a transverse field. We thus show that the description as a simpleIsing system is insufficient to quantitatively describe the full phase diagramof $\mathrm{LiHoF_4}$, for the pure as well as for the dilute system.

The Effect of Intrinsic Quantum Fluctuations on the Phase Diagram of Anisotropic Dipolar Magnets