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arXiv:2511.01646 · Entropy

On the Fibonacci-Lucas Ground State Degeneracies of the One-Dimensional Antiferromagnetic Ising Model at Criticality

Bastian Castorene, Francisco J. Peña, Patricio Vargas

cond-mat.stat-mechquant-phSubmitted Nov 3, 2025• Announced Nov 4, 2025• 1 citation
v1 · Nov 3, 2025v2 · Apr 26, 2026
arXivHTMLPDF

Abstract

This work examines the one-dimensional antiferromagnetic Ising model in a longitudinal magnetic field, comparing open-chain and closed-ring geometries. At the nontrivial quantum critical point (QCP) $B_{\mathrm{crit}} = B/J = 2$, we perform a microcanonical analysis of the ground-state manifold and explicitly count the number of degenerate configurations. The enumeration reveals that ground states follow the $N$th Fibonacci sequence for open chains and the $N$th Lucas sequence for periodic rings, establishing a clear correspondence between critical degeneracy, topology, and the golden ratio. This combinatorial duality exposes a number-theoretic structure underlying quantum criticality and highlights the role of topological constraints in shaping residual entropy. Beyond its conceptual relevance, the result provides a compact framework for analyzing degeneracy scaling in one-dimensional spin systems and may inform future studies of critical phenomena and quantum thermodynamic devices operating near critical regimes.

Journal reference
Entropy 28, 821 (2026)
DOI
10.3390/e28070821
Comments
5 pages, 2 Fig

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