Pure ground states and symmetry breaking in short‑range spin glasses

Determine the number of pure ground states and characterize the nature of symmetry breaking in short‑range spin‑glass systems, such as the Edwards–Anderson model, to clarify their zero‑temperature phase structure.

Background

The paper reviews longstanding challenges in spin‑glass theory beyond the mean‑field regime, emphasizing that while replica symmetry breaking provides a mean‑field description, many basic structural features of short‑range systems remain unsettled.

In this context, the authors highlight that even fundamental quantities like the number of pure ground states and the character of symmetry breaking for short‑range spin glasses have not been pinned down, motivating their topological approach via the signed Laplacian.