  The Random-Field Ising Model (RFIM) has been extensively studied as a model
system for understanding the effects of disorder in magnets. Since the late
1970s, there has been a particular focus on realizations of the RFIM in
site-diluted antiferromagnets. We observe random-field effects in the dilute
dipole-coupled ferromagnet $\mathrm{LiHo}_x\mathrm{Y}_{1-x}\mathrm{F}_4$. In
the presence of a magnetic field transverse to the Ising axis ($H_t$), the
behavior of $\mathrm{LiHo}_x\mathrm{Y}_{1-x}\mathrm{F}_4$ becomes increasingly
dominated by the influence of random-field terms in the effective Hamiltonian.
This is seen experimentally in the shape of the ferromagentic-paramagnetic
phase boundary and in changes to the critical exponents near the classical
critical point. We find that above the classical critical point the magnetic
susceptibility diverges as $H_t\to0$, and that the susceptibility both above
and below the classical critical point can be collapsed onto a single universal
curve using a modified Curie law which explicitly incorporates random-field
contributions. The discovery of a ferromagnetic realization of the RFIM opens
the door to investigation of the random-field problem with the wide variety of
techniques available for probing ferromagnets, including the ability to examine
both the statics and dynamics of the random-field problem. It also allows
studying the effects of controlled amounts of randomness on the dynamics of
domain pinning and the energetics of domain reversal.
