  Using the event-chain Monte Carlo (MC) algorithm, we investigate phase
transitions of the stacked Kagome Heisenberg systems with classical vector
spins including up to the 3rd-nearest-neighbor couplings. In particular, we
focus on two types of non-coplanar spin orders ---cuboc1 and cuboc2 orders,
both of which have twelve-sublattice structures accompanying the
translational-symmetry breaking. We perform event-chain MC simulations up to
L=72, where L represents the linear dimension of the stacked Kagome lattice,
and then find that the cuboc1 transition shows 2nd-order-transition behaviors
with a tendency to a weak-1st-order transition up to L=72, while the cuboc2
transition is basically described by the 1st-order transition. We then discuss
the above transitions in connection with the effective Landau-Ginzburg-Wilson
theory with the O(3)xO(3) symmetry.
