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On-Site Potential Creates Complexity in Systems with Disordered Coupling
I Gershenzon1, B Lacroix-A-Chez-Toine1,2, O Raz1
1Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel.
Adding a weak nonlinear on-site potential drastically increases the number of critical points in many-body systems. This finding offers a comprehensive view of critical point organization in complex systems.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Complex Systems
Background:
- Understanding the energy landscape of many-body systems is crucial for various fields.
- Disordered two-body interactions are common in physical systems like spin glasses.
- The role of on-site potentials in shaping these landscapes is not fully understood.
Purpose of the Study:
- To calculate the average number of critical points (N[over ¯]) in disordered many-body systems.
- To investigate the impact of a weak nonlinear on-site potential on N[over ¯].
- To provide a detailed understanding of critical point organization.
Main Methods:
- Analytical calculation of the average number of critical points.
- Analysis of many-body systems with disordered two-body interactions.
- Inclusion of a weak nonlinear on-site potential in the model.
Main Results:
- A weak nonlinear on-site potential dramatically increases N[over ¯].
- The increase in N[over ¯] scales exponentially with system size.
- A complete picture of critical point organization was established.
Conclusions:
- Nonlinear on-site potentials significantly alter the complexity of energy landscapes.
- Results extend solvable spin-glass models to more realistic scenarios.
- Findings are relevant for glassy systems, nonlinear oscillator networks, and interacting many-body systems.
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