Stochastic resonance in the driven Ising model on small-world networks

Area of Science:

• Physics
• Statistical Mechanics
• Complex Networks

Background:

• Stochastic resonance (SR) is a phenomenon where a weak signal can be amplified by adding noise.
• The Ising model is a fundamental model in statistical mechanics for studying magnetism.
• Small-world networks exhibit unique topological properties, bridging regular and random networks.

Purpose of the Study:

• To investigate stochastic resonance phenomena in a field-driven Ising model on small-world networks.
• To analyze the effect of rewiring probability on the system's dynamic phase transitions and resonance behavior.
• To understand the influence of long-range interactions on resonance in different magnetic phases.

Main Methods:

• Monte Carlo dynamic simulations were employed to study the system's response.
• The magnetization of the Ising model was examined under an oscillating magnetic field.
• Rewiring probability was systematically varied to explore network topology effects.

Main Results:

• A dynamic phase transition was observed at a finite temperature for any finite rewiring probability.
• The system exhibited double resonance peaks, indicating complex resonance behavior.
• The resonance peak in the ferromagnetic phase increased with rewiring probability.
• The resonance peak in the paramagnetic phase decreased with rewiring probability.

Conclusions:

• Small-world network topology significantly influences stochastic resonance in the Ising model.
• Long-range interactions introduced by rewiring have opposing effects on resonance in the ferromagnetic and paramagnetic phases.
• The study reveals a rich interplay between network structure, phase transitions, and resonance phenomena.