Exploring Replica Symmetry Breaking and Topological Collapse in Spin Glasses with Quantum Annealing
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arXiv
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| Formato: | Preprint |
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2025
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| _version_ | 1866918223517057024 |
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| author | Ghosh, Kumar |
| author_facet | Ghosh, Kumar |
| contents | Replica symmetry breaking (RSB) underlies the complex organization of disordered systems, yet quantitative validation beyond $N \sim 100$ spins has remained computationally challenging. We use quantum annealing to access ground states of the Sherrington-Kirkpatrick model up to $N = 4000$ spins, enabling the most extensive test of Parisi's Nobel Prize-winning RSB solution to date. Five independent observables confirm RSB predictions: ground-state energies converge to Parisi's value with characteristic $N^{-2/3}$ corrections, energy fluctuations scale as $N^{-3/4}$ ($γ= 0.739 \pm 0.036$), the chaos exponent $θ= 0.51 \pm 0.02$ ($R^2 = 0.989$) confirms mean-field universality, the overlap distribution exhibits hierarchical structure ($σ_q = 0.19$), and the complexity remains invariant under 36\% network dilution. Beyond a critical threshold $0.8 < D_c < 0.9$, the hierarchy collapses discontinuously through a cooperative avalanche that converts the entire system to vacancies within a narrow parameter window $ΔD = 0.1$. These findings establish quantum computation as a tool for probing emergent many-body phenomena and uncover the topological foundations of complexity in disordered systems, with implications for neural networks, optimization, and materials science. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06403 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploring Replica Symmetry Breaking and Topological Collapse in Spin Glasses with Quantum Annealing Ghosh, Kumar Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons Computational Physics Quantum Physics Replica symmetry breaking (RSB) underlies the complex organization of disordered systems, yet quantitative validation beyond $N \sim 100$ spins has remained computationally challenging. We use quantum annealing to access ground states of the Sherrington-Kirkpatrick model up to $N = 4000$ spins, enabling the most extensive test of Parisi's Nobel Prize-winning RSB solution to date. Five independent observables confirm RSB predictions: ground-state energies converge to Parisi's value with characteristic $N^{-2/3}$ corrections, energy fluctuations scale as $N^{-3/4}$ ($γ= 0.739 \pm 0.036$), the chaos exponent $θ= 0.51 \pm 0.02$ ($R^2 = 0.989$) confirms mean-field universality, the overlap distribution exhibits hierarchical structure ($σ_q = 0.19$), and the complexity remains invariant under 36\% network dilution. Beyond a critical threshold $0.8 < D_c < 0.9$, the hierarchy collapses discontinuously through a cooperative avalanche that converts the entire system to vacancies within a narrow parameter window $ΔD = 0.1$. These findings establish quantum computation as a tool for probing emergent many-body phenomena and uncover the topological foundations of complexity in disordered systems, with implications for neural networks, optimization, and materials science. |
| title | Exploring Replica Symmetry Breaking and Topological Collapse in Spin Glasses with Quantum Annealing |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Strongly Correlated Electrons Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2511.06403 |