Critical line of the triangular Ising antiferromagnet in a field from a 
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-symmetric corner transfer matrix algorithm

Nyckees, Samuel; Rufino, Afonso; Mila, Frédéric; Colbois, Jeanne

doi:10.1103/physreve.108.064132

Phys. Rev. E

2023

DOI: 10.1103/physreve.108.064132

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Critical line of the triangular Ising antiferromagnet in a field from a C3 -symmetric corner transfer matrix algorithm

Samuel Nyckees,

Afonso Rufino,

Frédéric Mila

et al.

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2024

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Cited by 2 publications

References 102 publications

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Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices

Lukin,

Sotnikov

2024

Phys. Rev. E

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We develop a new methodology to contract tensor networks within the corner transfer matrix renormalization group approach for a wide range of two-dimensional lattice geometries. We discuss contraction algorithms on the example of triangular, kagome, honeycomb, square-octagon, star, ruby, square-hexagon-dodecahedron, and dice lattices. As benchmark tests, we apply the developed method to the classical Ising model on different lattices and observe a remarkable agreement of the results with the available from the literature. The approach also shows the necessary potential to be applied to various quantum lattice models in a combination with the wave-function variational optimization schemes. Published by the American Physical Society 2024

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Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices

Lukin,

Sotnikov

2024

Phys. Rev. E

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Tensor networks for hierarchical lattices

Akimenko,

Myshlyavtsev

2024

EPL

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In this paper, we propose an approach to obtain numerically exact solutions for hierarchical lattices by representing them as a tensor network. The visual representation of these networks greatly simplifies the computational algorithm. Furthermore, we introduce a method for incorporating single-node interactions, enabling us to disregard the inhomogeneity of the hierarchical lattice nodes and simulate the behavior on a regular lattice instead. This methodology allows for qualitative studies of the phase space of desired lattice models with single-node interactions, which holds relevance for adsorption systems. The efficiency of the approach is demonstrated using the Ising model and the binary gas adsorption model as examples.

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Critical line of the triangular Ising antiferromagnet in a field from a C3 -symmetric corner transfer matrix algorithm

Cited by 2 publications

References 102 publications

Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices

Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices

Tensor networks for hierarchical lattices

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