  Phase diagram of a discrete counterpart of the classical Heisenberg model,
the truncated tetrahedral model, is analyzed on the square lattice, when the
interaction is ferromagnetic. Each spin is represented by a unit vector that
can point to one of the 12 vertices of the truncated tetrahedron, which is a
continuous interpolation between the tetrahedron and the octahedron. Phase
diagram of the model is determined by means of the statistical analogue of the
entanglement entropy, which is numerically calculated by the corner transfer
matrix renormalization group method. The obtained phase diagram consists of
four different phases, which are separated by five transition lines. In the
parameter region, where the octahedral anisotropy is dominant, a weak
first-order phase transition is observed.
