Percolation in high dimensions is not understood

Abstract

The number of spanning clusters in four to nine dimensions does not fully follow the expected size dependence for random percolation.

9-dimensional data and more points for large lattices added; statistics improved, text expanded, table of exponents inserted

References in corpus (3)

• Critical Percolation in High Dimensions
• Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model
• A Geometrical Interpretation of Hyperscaling Breaking in the Ising Model

Cited by in corpus (4)

• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Fisher's scaling relation above the upper critical dimension
• Universal Finite-Size Scaling for Percolation Theory in High Dimensions
• Number of spanning clusters at the high-dimensional percolation thresholds