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.
HYPERTILING -- a high performance Python library for the generation and visualization of hyperbolic lattices
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abstract
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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2025 1verdicts
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Classical spin liquids from frustrated Ising models in hyperbolic space
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.