  In the quest to realize a quantum spin liquid (QSL), magnetic long-range
order is hardly welcome. Yet it can offer deep insights into a complex world of
strong correlations and fluctuations. Much hope was placed in the cubic
pyrochlore Yb$_2$Ti$_2$O$_7$ as a putative U(1) QSL but a new class of
ultra-pure single crystals make it abundantly clear the stoichiometric compound
is a ferromagnet. Here we present a detailed experimental and theoretical study
of the corresponding field-temperature phase diagram. We find it to be richly
anisotropic with a critical endpoint for $\vec{B}\,\parallel\,\langle
100\rangle$, while field parallel to $\langle 110 \rangle$ and $\langle 111
\rangle$ enhances the critical temperature by up to a factor of two and shifts
the onset of the field-polarized state to finite fields. Landau theory shows
that Yb$_2$Ti$_2$O$_7$ in some ways is remarkably similar to pure iron.
However, it also pinpoints anomalies that cannot be accounted for at the
classical mean-field level including a dramatic enhancement of $T_{\mathrm{C}}$
and reentrant phase boundary by fields with a component transverse to the easy
axes, as well as the anisotropy of the upper critical field in the quantum
limit.
