  We study the properties of a two-body random matrix ensemble for
distinguishable spins. We require the ensemble to be invariant under the group
of local transformations and analyze a parametrization in terms of the group
parameters and the remaining parameters associated with the "entangling" part
of the interaction. We then specialize to a spin chain with nearest neighbour
interactions and numerically find a new type of quantum phase transition
related to the strength of a random external field i.e. the time reversal
breaking one body interaction term.
