Site percolation on the diamond hierarchical lattice shows a BKT-type essential singularity in correlation length at p_c, producing a critical phase with continuously varying fractal exponent ψ(p) for the largest cluster.
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Discrete harmonic morphisms ensure exact random-walk projection under network coarse-graining, and Laplacian renormalization often produces exact instances of them on real networks.
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Berezinskii-Kosterlitz-Thouless-type Transition in Site Percolation on the Diamond Hierarchical Lattice
Site percolation on the diamond hierarchical lattice shows a BKT-type essential singularity in correlation length at p_c, producing a critical phase with continuously varying fractal exponent ψ(p) for the largest cluster.
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Harmonic morphisms and dynamical invariants in network renormalization
Discrete harmonic morphisms ensure exact random-walk projection under network coarse-graining, and Laplacian renormalization often produces exact instances of them on real networks.