  We use finite connectivity equilibrium replica theory to solve models of
finitely connected unit-length vectorial spins, with random pair-interactions
which are of the orthogonal matrix type. Since the spins are continuous and the
connectivity c remains finite in the thermodynamic limit, the replica-symmetric
order parameter is a functional. The general theory is developed for arbitrary
values of the dimension d of the spins, and arbitrary choices of the ensemble
of random orthogonal matrices. We calculate phase diagrams and the values of
moments of the order parameter explicitly for d=2 (finitely connected XY spins
with random chiral interactions) and for d=3 (finitely connected classical
Heisenberg spins with random chiral interactions). Numerical simulations are
shown to support our predictions quite satisfactorily.

Disordered Systems and Neural Networks