  We present a magnetic phase diagram of rare-earth pyrochlore
$\rm{Yb_2Ti_2O_7}$ in a $\langle 111 \rangle$ magnetic field. Using heat
capacity, magnetization, and neutron scattering data, we show an unusual
field-dependence of a first-order phase boundary, wherein a small applied field
increases the ordering temperature. The zero-field ground state has
ferromagnetic domains, while the spins polarize along $\langle 111 \rangle$
above 0.65T. A classical Monte Carlo analysis of published Hamiltonians does
account for the critical field in the low T limit. However, this analysis fails
to account for the large bulge in the reentrant phase diagram, suggesting that
either long-range interactions or quantum fluctuations govern low field
properties.
