  We consider an alternative to the usual spin glass paradigm for disordered
magnetism, consisting of the previously unstudied combination of frustrated
magnetic interactions and pseudo-dipolar disorder in spin positions. We argue
that this model represents a general limiting case for real systems as well as
a realistic model for certain binary fluorides and oxides. Furthermore, it is
of great relevance to the highly topical subjects of the Coulomb phase and
`charge ice'. We derive an analytical solution for the ground state phase
diagram of a model system constructed in this paradigm and identify magnetic
phases that remain either disordered or partially ordered even at zero
temperature. These phases are of a hitherto unobserved type, but may be broadly
classified as either `spin liquids' or `semi-spin liquids' in contrast to the
usual spin glass or semi-spin glass. Numerical simulations are used to show
that the spin liquid phase exhibits no spin glass transition at finite
temperature, despite the combination of frustration and disorder. By mapping
onto a model of uncoupled loops of Ising spins, we show that the magnetic
structure factor of this phase acts, in the limit $T\rightarrow0$, as a
sensitive probe of the positional disorder correlations. We suggest that this
result can be generalized to more complex systems, including experimental
realizations of canonical spin glass models.
