On-Site Potential Creates Complexity in Systems with Disordered Coupling

Igor Gershenzon, Bertrand Lacroix A Chez Toine, Oren Raz, Eliran Subag, Ofer Zeitouni

Research output: Contribution to journalArticlepeer-review


We calculate the average number of critical points N¯ 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¯ 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.

Original languageEnglish
Article number237103
Pages (from-to)237103
Number of pages1
JournalPhysical Review Letters
Issue number23
Publication statusPublished - 9 Jun 2023


  • Disordered systems
  • Random & disordered media
  • Glassy systems
  • Random matrix theory
  • Statistical Physics


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