  In the context of a discrete analogue of the classical Heisenberg model, we
investigate critical behavior of the icosahedron model, where the interaction
energy is defined as the inner product of neighboring vector spins of unit
length pointing to vertices of the icosahedron. Effective correlation length
and magnetization of the model are calculated by means of the corner-transfer
matrix renormalization group (CTMRG) method. Scaling analysis with respect to
the cutoff dimension $m$ in CTMRG reveals the second-order phase transition
characterized by the exponents $\nu = 1.62\pm0.02$ and $\beta = 0.12\pm0.01$.
We also extract the central charge from the classical analogue of the
entanglement entropy as $c = 1.90\pm0.02$, which cannot be explained by the
minimal series of conformal field theory.
