Field-Driven Transitions in the Dipolar Pyrochlore Antiferromagnet Gd${}_2$Ti${}_2$O${}_7$

We present a mean-field theory for magnetic field driven transitions in dipolar coupled gadolinium titanate Gd${}_2$Ti${}_2$O${}_7$ pyrochlore system. Low temperature neutron scattering yields a phase that can be regarded as a 8 sublattice antiferromagnet, in which long-ranged ordered moments and fluctuating moments coexist. Our theory gives parameter regions where such a phase is realized, and predicts several other phases, with transitions amongst them driven by magnetic field as well as temperature. We find several instances of {\em local} disorder parameters describing the transitions.