  Exactly soluble spin-$\frac{1}2$ models on three-dimensional lattices are
proposed by generalizing Kitaev model on honeycomb lattice to three dimensions
with proper periodic boundary conditions. The simplest example is spins on a
diamond lattice which is exactly soluble. The ground state sector of the model
may be mapped into a p-wave paired state on cubic lattice. We observe for the
first time a topological phase transition from a gapless phase to a gapped
phase in an exactly soluble spin model. Furthermore, the gapless phase can not
be gapped by a perturbation breaking the time reversal symmetry. Unknotted and
unlinked Wilson loops arise as eigen excitations, which may evolute into linked
and knotted loop excitations. We show that these closed string excitations obey
abelian statistics in the gapped phase and non-abelian statistics in the
gapless phase.
