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arXiv:2202.05579 · Journal of Statistical Physics

Universality of Replica-Symmetry Breaking in the Transverse Field Sherrington–Kirkpatrick Model

Chigak Itoi, H. Ishimori, K. Sato, Y. Sakamoto

Published Feb 10, 2023• 3 citations
arXivHTMLPDF
DOI
10.1007/s10955-023-03078-7

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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.