On-Site Potential Creates Complexity in Systems with Disordered Coupling.
PHYSICAL REVIEW LETTERS 2023;
130:237103. [PMID:
37354403 DOI:
10.1103/physrevlett.130.237103]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2022] [Accepted: 04/04/2023] [Indexed: 06/26/2023]
Abstract
We calculate the average number of critical points N[over ¯] of the energy landscape of a many-body system with disordered two-body interactions and a weak on-site potential. We find that introducing a weak nonlinear on-site potential dramatically increases N[over ¯] to exponential in system size and give a complete picture of the organization of critical points. Our results extend solvable spin-glass models to physically more realistic models and are of relevance to glassy systems, nonlinear oscillator networks, and many-body interacting systems.
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