Critical behavior of the two-dimensional icosahedron model

Abstract

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 $\nu =1.62\pm 0.02$ and $\beta =0.12\pm 0.01$. We also extract the central charge from the classical analogue of the entanglement entropy as $c=1.90\pm 0.02$, which cannot be explained by the minimal series of conformal field theory.

arXiv comment6 pages, 5 figures

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Cited by in corpus (8)

• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• Finite-size and finite bond dimension effects of tensor network renormalization
• Finite-$m$ scaling analysis of Berezinskii-Kosterlitz-Thouless phase transitions and entanglement spectrum for the six-state clock model
• Tensor Network Based Finite-Size Scaling for Two-Dimensional Classical Models
• Absence of logarithmic divergence of the entanglement entropies at the phase transitions of a 2D classical hard rod model
• Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model
• Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group