  We study phase transition behavior of the Heisenberg model on a distorted
triangular lattice with competing interactions. The ground-state phase diagram
indicates that underlying symmetry can be changed by tuning parameters. We
focus on two cases in which a phase transition with discrete symmetry breaking
occurs. The first is that the order parameter space is SO(3)$\times C_3$. In
this case, a first-order phase transition, with threefold symmetry breaking,
occurs. The second has the order parameter space SO(3)$\times Z_2$. In this
case, a second-order phase transition occurs with twofold symmetry breaking. To
investigate finite-temperature properties of these phase transitions from a
microscopic viewpoint, we introduce a method to make the connection between
continuous frustrated spin systems and the Potts model with invisible states.
