English

On-Site Potential Creates Complexity in Systems with Disordered Coupling

Disordered Systems and Neural Networks 2023-06-21 v2 Statistical Mechanics Mathematical Physics math.MP

Abstract

We calculate the average number of critical points N\overline{\mathcal{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\overline{\mathcal{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.

Keywords

Cite

@article{arxiv.2206.10554,
  title  = {On-Site Potential Creates Complexity in Systems with Disordered Coupling},
  author = {Igor Gershenzon and Bertrand Lacroix-A-Chez-Toine and Oren Raz and Eliran Subag and Ofer Zeitouni},
  journal= {arXiv preprint arXiv:2206.10554},
  year   = {2023}
}
R2 v1 2026-06-24T11:58:51.967Z