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Mean-field behavior of the negative-weight percolation model on random regular graphs
Oliver Melchert1, Alexander K Hartmann, Marc Mézard
1Institute of Physics, University of Oldenburg, D-26111 Oldenburg, Germany. oliver.melchert@uni-oldenburg.de
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
This study confirms the upper critical dimension of six for negative-weight percolation on random graphs. Analytical and numerical methods agree on phase transitions and critical exponents, finding no glass phase.
Area of Science:
- Statistical physics
- Network science
- Percolation theory
Background:
- The negative-weight percolation model on random graphs is studied to understand mean-field behavior.
- A bimodal weight distribution and fixed connectivity are employed.
Purpose of the Study:
- To analytically and numerically investigate minimum-weight loops in this model.
- To confirm the conjectured upper critical dimension and analyze phase transitions.
Main Methods:
- Analytical approach based on a conjectured equivalence with self-avoiding walks in a random medium.
- Numerical approach using a mapping to a minimum-weight matching problem.
Main Results:
- Agreement between analytical and numerical results on phase transition location and critical exponents.
- Absence of significant indications of a glass phase.
- Confirmation of the upper critical dimension at d(u)=6.
Conclusions:
- The study validates theoretical predictions regarding percolation models on random graphs.
- The findings contribute to understanding critical phenomena in complex networks.
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