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

中文翻译：

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现场电位会导致耦合无序的系统变得复杂

我们计算临界点的平均数量$\stackrel{￣}{\mathcal{氮}}$具有无序两体相互作用和弱现场势的多体系统的能量景观。我们发现引入弱非线性现场电势会显着增加$\stackrel{￣}{\mathcal{氮}}$使系统规模呈指数级增长，并给出关键点组织的完整画面。我们的结果将可解的自旋玻璃模型扩展到物理上更真实的模型，并且与玻璃系统、非线性振荡器网络和多体相互作用系统相关。