We have measured the magnetic correlations, susceptibility, specific heat, and thermal relaxation in the dipolar-coupled Ising system LiHo_xY_(1-x)F_4. The material is ferromagnetic for spin concentrations at least as low as x=0.46, with a Curie temperature obeying mean-field scaling relative to that of pure LiHoF_4. In contrast, an x=0.167 sample behaves as a spin glass above its transition temperature, while an x=0.045 crystal shows very different glassy properties characterized by decreasing barriers to relaxation and nonexponential thermal relaxation as T→0. We find the properties of the x=0.045 system to be consistent with a single low-degeneracy ground state with a large gap for excitations. The x=0.167 sample, however, supports a complex ground state with no appreciable gap, in accordance with prevailing theories of spin glasses. The underlying causes of such disparate behavior are discussed in terms of random clusters as probed by neutron studies of the x=0.167 sample.
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