On-Site Potential Creates Complexity in Systems with Disordered Coupling

TL;DR

This paper demonstrates that adding a weak on-site potential to disordered many-body systems exponentially increases the number of critical points in their energy landscape, revealing complex organization relevant to various physical systems.

Contribution

It extends solvable spin-glass models by analyzing the impact of weak nonlinear on-site potentials on critical point complexity.

Findings

Weak on-site potential causes exponential growth in critical points

Complete organization of critical points is characterized

Results applicable to glassy systems and nonlinear networks

Abstract

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.