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HYPERTILING -- a high performance Python library for the generation and visualization of hyperbolic lattices

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arxiv 2309.10844 v3 pith:F7VFVPEU submitted 2023-09-19 physics.comp-ph hep-lat

Manuel Schrauth , Yanick Thurn , Florian Goth , Jefferson S. E. Portela , Dietmar Herdt , Felix Dusel This is my paper · ORCID
classification physics.comp-phhep-lat
keywords hyperbolicgenerationhypertilinglatticeslibrarypythonverticesvisualization
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HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincar\'e disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs. In this manuscript, we present a comprehensive exploration of the package, encompassing its mathematical foundations, usage examples, applications, and a detailed description of its implementation.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices

    cond-mat.mes-hall 2026-01 conditional novelty 6.0 of 10

    Boundary two-point correlations on hyperbolic lattices remain almost power-law up to about 90% hexagon defects, suggesting that smaller defective lattices can substitute for pure hyperbolic lattices.

  2. Classical spin liquids from frustrated Ising models in hyperbolic space

    cond-mat.str-el 2025-06 accept novelty 6.0 of 10

    Ising spins on frustrated hyperbolic lattices realize classical spin liquids with a finite residual entropy, and the boundary shape selects between disordered and ordered ground states.

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