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Boolean decision problems with competing interactions on scale-free networks: critical thermodynamics
Helmut G Katzgraber1, Katharina Janzen, Creighton K Thomas
1Department of Physics and Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA.
Summary
Boolean variables on scale-free networks exhibit stable phases, with transitions depending on interaction decay. This research clarifies spin glass behavior and universality in complex systems.
Area of Science:
- Statistical physics
- Network science
- Computational complexity
Background:
- Scale-free networks are common in nature and technology.
- Ising spin glasses model complex systems with competing interactions.
- Understanding critical behavior is key to predicting system stability.
Purpose of the Study:
- To investigate the critical behavior of Boolean variables on scale-free networks with competing interactions.
- To determine the phase diagram based on the disorder-network-decay-exponent.
- To analyze the universality of spin glasses on these networks.
Main Methods:
- Analytical calculations of the phase diagram.
- Monte Carlo simulations for verification.
- Analysis of Boolean decision problem stability.
Main Results:
- A finite-temperature spin-glass transition occurs when the decay exponent is > 3.
- For decay exponents <= 3, the spin-glass phase is stable at all temperatures.
- Both ferromagnetic and spin-glass phases show robustness to perturbations.
- Universality is observed for spin glasses on scale-free networks with a given decay exponent.
Conclusions:
- Boolean decision problems on scale-free networks are stable to local perturbations.
- For decay exponents > 4, the universality class matches the Sherrington-Kirkpatrick model.
- The study provides insights into the behavior of complex systems with competing interactions.
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