Emergent spectral geometry in the Coherence--Curvature Model
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908661674147840 |
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| author | Lamas, Jorge |
| author_facet | Lamas, Jorge |
| contents | We investigate the Coherence--Curvature Model (CCM), a dynamical ensemble of connected graphs governed by a Hamiltonian that couples algebraic connectivity, Ollivier-Ricci curvature, and an edge-density penalty. Using connected simulated annealing we generate low-energy graph configurations and characterize their emergent geometry through the spectral dimension (ds), the Hausdorff dimension (dh), and the average distance. Finite-size scaling shows a clear growth of ds with system size, while dh increases more mildly. At the largest volumes explored the data are compatible with ds ~ 4 and dh ~ 3, implying ds > dh and a nontrivial hierarchy between spectral and volumetric notions of dimension. We also map the dependence on the curvature coupling gamma and the locality coupling beta, and we find a slow power-law growth of typical distances with a small exponent eta. The CCM therefore provides a controlled numerical laboratory in which the interplay of coherence, curvature, and locality yields finite-dimensional, fractal-like geometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13423 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Emergent spectral geometry in the Coherence--Curvature Model Lamas, Jorge General Relativity and Quantum Cosmology High Energy Physics - Theory We investigate the Coherence--Curvature Model (CCM), a dynamical ensemble of connected graphs governed by a Hamiltonian that couples algebraic connectivity, Ollivier-Ricci curvature, and an edge-density penalty. Using connected simulated annealing we generate low-energy graph configurations and characterize their emergent geometry through the spectral dimension (ds), the Hausdorff dimension (dh), and the average distance. Finite-size scaling shows a clear growth of ds with system size, while dh increases more mildly. At the largest volumes explored the data are compatible with ds ~ 4 and dh ~ 3, implying ds > dh and a nontrivial hierarchy between spectral and volumetric notions of dimension. We also map the dependence on the curvature coupling gamma and the locality coupling beta, and we find a slow power-law growth of typical distances with a small exponent eta. The CCM therefore provides a controlled numerical laboratory in which the interplay of coherence, curvature, and locality yields finite-dimensional, fractal-like geometries. |
| title | Emergent spectral geometry in the Coherence--Curvature Model |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.13423 |