• Open Access

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

Hiroshi Ueda, Kouichi Okunishi, Seiji Yunoki, and Tomotoshi Nishino
Phys. Rev. E 102, 032130 – Published 18 September 2020

Abstract

We investigate the phase transition of the dodecahedron model on the square lattice. The model is a discrete analog 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 Tc=0.4398(8) with the critical exponents ν=2.88(8) and β=0.21(1). The central charge of the system is estimated as c=1.99(6).

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  • Received 20 April 2020
  • Accepted 3 September 2020

DOI:https://doi.org/10.1103/PhysRevE.102.032130

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

©2020 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Hiroshi Ueda1,2, Kouichi Okunishi3, Seiji Yunoki1,4,5, and Tomotoshi Nishino6

  • 1Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS), Kobe 650-0047, Japan
  • 2JST, PRESTO, Kawaguchi, 332-0012, Japan
  • 3Department of Physics, Niigata University, Niigata 950-2181, Japan
  • 4Computational Condensed Matter Physics Laboratory, RIKEN Cluster for Pioneering Research (CPR), Wako, 351-0198, Japan
  • 5Computational Quantum Matter Research Team, RIKEN Center for Emergent Matter Science (CEMS), Wako, 351-0198, Japan
  • 6Department of Physics, Graduate School of Science, Kobe University, Kobe 657-8501, Japan

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Issue

Vol. 102, Iss. 3 — September 2020

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