Ising model on Fibonacci lattices: ring topology of sphere, cut ring, and torus

We study the Ising model on two-dimensional surfaces discretized using the Fibonacci method with Delaunay triangulation, considering the ring, cut ring, and torus topologies. The phase diagrams reveal a universal critical temperature of T_C ≈ 3.33 (3)J in the thermodynamic limit, which is consistent with the results for the Fibonacci sphere [1]. Despite the exclusion of topological defects (vertices with coordination numbers 5/7) in the ring and cut ring Fibonacci configurations, deviations from the critical temperature of the ideal flat triangular lattice are observed. The T_C values, similar to the spherical case, experience shifts. Notably, the torus, which possesses the minimal defect density (<1%), exhibits smooth convergence and negligible finite-size shifts in T_C. These results underscore the interplay between local connectivity and global topology in shaping critical phenomena.