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Bibliographic Details
Main Authors: Itoi, C., Fujiwara, K., Sakamoto, Y.
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2403.02699
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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