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Mathematical Physics
Title: Existence of de Almeida-Thouless-type instability in the transverse field Sherrington-Kirkpatrick model
(Submitted on 5 Mar 2024 (v1), last revised 13 Mar 2024 (this version, v2))
Abstract: 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.
Submission history
From: Yoshinori Sakamoto [view email][v1] Tue, 5 Mar 2024 06:37:17 GMT (12kb)
[v2] Wed, 13 Mar 2024 04:26:50 GMT (13kb)
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