  We study a finite-temperature phase transition in the two-dimensional
classical Heisenberg model on a triangular lattice with a ferromagnetic
nearest-neighbor interaction $J_1$ and an antiferromagnetic
third-nearest-neighbor interaction $J_3$ using a Monte Carlo method. Apart from
a trivial degeneracy corresponding to O(3) spin rotations,the ground state for
$J_3 \neq 0$ has a threefold degeneracy corresponding to 120 degree lattice
rotations. We find that this model exhibits a first-order phase transition with
the breaking of the threefold symmetry when the interaction ratio is
$J_3/J_1=-3$.
