Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.02699 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914712755634176 |
|---|---|
| author | Itoi, C. Fujiwara, K. Sakamoto, Y. |
| author_facet | Itoi, C. Fujiwara, K. Sakamoto, Y. |
| contents | The interpolation method for mean field spin glass models developed by Guerra and Talagrand is extended to a quantum mean field spin glass model. This extension enables us to obtain both replica-symmetric (RS) and one step replica-symmetry breaking (1RSB) solutions of the free energy density in the transverse field Sherrington-Kirkpatrick model. It is shown that the RS solution is exact in the paramagnetic phase. We provide a sufficient condition on coupling constants where the 1RSB solution gives better bound than the RS one. This condition reduced to physical quantities in disordered single spin systems allows a simple computer-assisted proof for the existence of the de Almeida-Thouless-type instability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02699 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of de Almeida-Thouless-type instability in the transverse field Sherrington-Kirkpatrick model Itoi, C. Fujiwara, K. Sakamoto, Y. Mathematical Physics Disordered Systems and Neural Networks The interpolation method for mean field spin glass models developed by Guerra and Talagrand is extended to a quantum mean field spin glass model. This extension enables us to obtain both replica-symmetric (RS) and one step replica-symmetry breaking (1RSB) solutions of the free energy density in the transverse field Sherrington-Kirkpatrick model. It is shown that the RS solution is exact in the paramagnetic phase. We provide a sufficient condition on coupling constants where the 1RSB solution gives better bound than the RS one. This condition reduced to physical quantities in disordered single spin systems allows a simple computer-assisted proof for the existence of the de Almeida-Thouless-type instability. |
| title | Existence of de Almeida-Thouless-type instability in the transverse field Sherrington-Kirkpatrick model |
| topic | Mathematical Physics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2403.02699 |