Exact Ground States of Two Dimensional $\pm J$ Spin Glasses
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915234686435328 |
|---|---|
| author | Song, Chaoming |
| author_facet | Song, Chaoming |
| contents | We derive exact analytical expressions for the ground-state energy and entropy of the two-dimensional $\pm J$ Ising spin glass, uncovering a nested hierarchy of frustrations. Each level in this hierarchy contributes through the kernel and pseudo-determinant of effective operators, capturing the energy and entropy, respectively. At leading order, the structure coincides with geometric plaquette frustrations, while subleading corrections arise from magnetic adjacency matrices defined on percolated clusters in the dual lattice. Our results, supported by numerical simulations, provide a systematic framework for analyzing spin-glass ground states and offer new insight into glass order in finite dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06953 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact Ground States of Two Dimensional $\pm J$ Spin Glasses Song, Chaoming Disordered Systems and Neural Networks Statistical Mechanics We derive exact analytical expressions for the ground-state energy and entropy of the two-dimensional $\pm J$ Ising spin glass, uncovering a nested hierarchy of frustrations. Each level in this hierarchy contributes through the kernel and pseudo-determinant of effective operators, capturing the energy and entropy, respectively. At leading order, the structure coincides with geometric plaquette frustrations, while subleading corrections arise from magnetic adjacency matrices defined on percolated clusters in the dual lattice. Our results, supported by numerical simulations, provide a systematic framework for analyzing spin-glass ground states and offer new insight into glass order in finite dimensions. |
| title | Exact Ground States of Two Dimensional $\pm J$ Spin Glasses |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2504.06953 |