Constraint percolation on hyperbolic lattices

Lopez, Jorge H Y Schwarz, J M (2017) Constraint percolation on hyperbolic lattices. Physical Review E, 96 (052108). 052108-1-052108-10. ISSN 2470-0053

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Resumen

Hyperbolic lattices interpolate between finite-dimensional lattices and Bethe lattices, and they are interesting in their own right, with ordinary percolation exhibiting not one but two phase transitions.We study four constraint percolation models—k-core percolation (for k = 1,2,3) and force-balance percolation—on several tessellations of the hyperbolic plane. By comparing these four different models, our numerical data suggest that all of the k-core models, even for k = 3, exhibit behavior similar to ordinary percolation, while the force-balance percolation transition is discontinuous. We also provide proof, for some hyperbolic lattices, of the existence of a critical probability that is less than unity for the force-balance model, so that we can place our interpretation of the numerical data for this model on a more rigorous footing. Finally, we discuss improved numerical methods for determining the two critical probabilities on the hyperbolic lattice for the k-core percolation models.

Tipo de Elemento:	Artículo
Asunto:	Q Ciencias > QC Physics
Division:	Facultad de Ciencias Exactas y Naturales > Programa de Física > Productividad
Depósito de Usuario:	PhD Jorge Hernán López Melo
Fecha Deposito:	08 Nov 2023 19:45
Ultima Modificación:	08 Nov 2023 19:45
URI:	http://sired.udenar.edu.co/id/eprint/9267

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