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arXiv · 2004.08669

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

Hiroshi Ueda·Kouichi Okunishi·Seiji Yunoki·Tomotoshi Nishino
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Abstract

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 $T^{~}_{\rm c}=0.4398(8)$ with the critical exponents $\nu=2.88(8)$ and $\beta=0.21(1)$. The central charge of the system is estimated as $c=1.99(6)$.

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Hiroshi Ueda, Kouichi Okunishi, Seiji Yunoki, Tomotoshi Nishino. 2020-04-18. Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model. https://doi.org/10.1103/physreve.102.032130

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