Critical behavior of the two-dimensional icosahedron model

In the context of a discrete analog of the classical Heisenberg model, we investigate the 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 the vertices of the icosahedron. The effective correlation length and magnetization of the model are calculated by means of the corner-transfer-matrix renormalization group (CTMRG) method. A scaling analysis with respect to the cutoff dimension m in CTMRG reveals a second-order phase transition characterized by the exponents ν=1.62±0.02 and β=0.12±0.01. We also extract the central charge from the classical analog of entanglement entropy as c=1.90±0.02, which cannot be explained by the minimal series of conformal field theory.