On the Replica Symmetric Solution in General Diluted Spin Glasses
Fuente:
Wiley Open Access
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Artículo Open Access |
| Publié: |
Wiley
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1867008450946400256 |
|---|---|
| author | Ratul Biswas Wei‐Kuo Chen Arnab Sen |
| author_facet | Ratul Biswas Wei‐Kuo Chen Arnab Sen Ratul Biswas Wei‐Kuo Chen Arnab Sen |
| collection | Wiley Open Access |
| contents | On the Replica Symmetric Solution in General Diluted Spin Glasses Ratul Biswas Wei‐Kuo Chen Arnab Sen Random Structures & Algorithms ABSTRACTWe present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random ‐uniform hypergraphs with sparsity parameter . Our result shows that there exist two key regimes in which the model exhibits replica symmetry and the free energy can be explicitly represented as the evaluation of an energy functional at the unique fixed point of a recursive distributional equation. One is called the high‐temperature regime, where the temperature and the sparsity parameter are essentially inversely proportional to each other; the other is the subcritical regime defined as . In particular, the fact that the second regime is independent of the temperature parameter further allows us to deduce an analogous representation of the ground state energy in the subcritical regime. Along the way, we revisit several well‐known formulas and also derive new ones for the free and ground state energies in the constraint satisfaction problem, Potts model, XY model, and continuous hardcore model. 10.1002/rsa.70013 http://creativecommons.org/licenses/by/4.0/ |
| doi_str_mv | 10.1002/rsa.70013 |
| format | Artículo Open Access |
| id | wiley_oa_10_1002_rsa_70013 |
| institution | Wiley Open Access |
| license_str_mv | http://creativecommons.org/licenses/by/4.0/ |
| publishDate | 2025 |
| publisher | Wiley |
| record_format | wiley_oa |
| spellingShingle | On the Replica Symmetric Solution in General Diluted Spin Glasses Ratul Biswas Wei‐Kuo Chen Arnab Sen Random Structures & Algorithms On the Replica Symmetric Solution in General Diluted Spin Glasses Ratul Biswas Wei‐Kuo Chen Arnab Sen Random Structures & Algorithms ABSTRACTWe present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random ‐uniform hypergraphs with sparsity parameter . Our result shows that there exist two key regimes in which the model exhibits replica symmetry and the free energy can be explicitly represented as the evaluation of an energy functional at the unique fixed point of a recursive distributional equation. One is called the high‐temperature regime, where the temperature and the sparsity parameter are essentially inversely proportional to each other; the other is the subcritical regime defined as . In particular, the fact that the second regime is independent of the temperature parameter further allows us to deduce an analogous representation of the ground state energy in the subcritical regime. Along the way, we revisit several well‐known formulas and also derive new ones for the free and ground state energies in the constraint satisfaction problem, Potts model, XY model, and continuous hardcore model. 10.1002/rsa.70013 http://creativecommons.org/licenses/by/4.0/ |
| title | On the Replica Symmetric Solution in General Diluted Spin Glasses |
| topic | Random Structures & Algorithms |
| url | https://onlinelibrary.wiley.com/doi/10.1002/rsa.70013 |