Researchers Explore Spectral Origin of the Topological Gap Exponent

A theoretical preprint published on arXiv presents a derivation of the spectral origin of the topological gap exponent d + eta in critical point clouds. The work analyzes excess H1 total persistence relative to density-matched null baselines.

The researchers demonstrated analytically that the spectral integral decomposes into a volume term and a shape factor related to anomalous dimension. They proved that the mechanism requires infrared dominance (d < 2 + eta), which confines it to d = 2 for physical systems, while in d = 3 the integral is ultraviolet-dominated, explaining why density normalization is required.

Empirical parameter sweeps for the Potts model (q = 4) across sizes L = 32 to 256 provided initial estimates, though the authors note these findings remain tentative pending confirmation on larger lattices of L >= 1024.