Existence of de Almeida-Thouless-type instability in the transverse field Sherrington-Kirkpatrick model
- Resource Type
- Working Paper
- Authors
- Itoi, C.; Fujiwara, K.; Sakamoto, Y.
- Source
- Subject
- Mathematical Physics
Condensed Matter - Disordered Systems and Neural Networks
- Language
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.
Comment: 12 pages