A Parisi Formula for Quantum Spin Glasses
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914709220884480 |
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| author | Manai, Chokri Warzel, Simone |
| author_facet | Manai, Chokri Warzel, Simone |
| contents | We establish three equivalent versions of a Parisi formula for the free energy of mean-field spin glasses in a transversal magnetic field. These results are derived from available results for classical vector spin glasses by an approximation method using the functional integral representation of the partition function. In this approach, the order parameter is a non-decreasing function with values in the non-negative, real hermitian Hilbert-Schmidt operators. For the quantum Sherrington-Kirkpatrick model, we also show that under the assumption of self-averaging of the self-overlap, the optimising Parisi order parameter is found within a two-dimensional subspace spanned by the self-overlap and the fully stationary overlap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06155 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Parisi Formula for Quantum Spin Glasses Manai, Chokri Warzel, Simone Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics 82D30, 82B10, 82B44 We establish three equivalent versions of a Parisi formula for the free energy of mean-field spin glasses in a transversal magnetic field. These results are derived from available results for classical vector spin glasses by an approximation method using the functional integral representation of the partition function. In this approach, the order parameter is a non-decreasing function with values in the non-negative, real hermitian Hilbert-Schmidt operators. For the quantum Sherrington-Kirkpatrick model, we also show that under the assumption of self-averaging of the self-overlap, the optimising Parisi order parameter is found within a two-dimensional subspace spanned by the self-overlap and the fully stationary overlap. |
| title | A Parisi Formula for Quantum Spin Glasses |
| topic | Disordered Systems and Neural Networks Statistical Mechanics Mathematical Physics 82D30, 82B10, 82B44 |
| url | https://arxiv.org/abs/2403.06155 |