  We study some properties of the dynamical realization of isolated left orders
of a countable group G. We show that the dynamical realization admits a unique
minimal set provided G is not infinite cyclic. We show that convex subgroup of
an isolated left order is finite in number. Using this, we give a dynamical
proof of the Tararin theorem. We also show that there is a new isolated order
on the braid group B_3.
