Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model

We investigate the phase transition of the dodecahedron model on the square lattice. The model is a discrete analogue of the classical Heisenberg model, which has continuous $O(3)$ symmetry. In order to treat the large on-site degree of freedom $q = 20$, we develop a massively parallelized numerical algorithm for the corner transfer matrix renormalization group method, incorporating EigenExa, the high-performance parallelized eigensolver. The scaling analysis with respect to the cutoff dimension reveals that there is a second-order phase transition at $T^{~}_{\rm c}=0.4403(4)$ with the critical exponents $\nu=2.88(5)$ and $\beta=0.22(1)$. The central charge of the system is estimated as $c=1.98(4)$.