First-order phase transition in a majority-vote model with inertia

Area of Science:

• Statistical physics
• Complex systems

Background:

• The majority-vote model is a fundamental concept in understanding collective behavior and phase transitions.
• Traditional models often assume spin-flip probability depends solely on neighbors' states.

Purpose of the Study:

• To generalize the majority-vote model by introducing inertia into spin-flip dynamics.
• To investigate the impact of individual spin state on flip probability.
• To analyze the resulting phase transitions and their characteristics.

Main Methods:

• Generalization of the majority-vote model with added inertia.
• Numerical calculation of transition rates using rare-event sampling.
• Development of a mean-field theory for analytical insights.

Main Results:

• Introduction of inertia alters the order-disorder phase transition from second-order to first-order (discontinuous).
• An 'explosive' transition is observed above a critical inertia level.
• Significant hysteresis behavior emerges, dependent on noise intensity.
• Coexistence of disordered and two symmetric ordered phases within the hysteresis loop.

Conclusions:

• Inertia is a critical factor that can fundamentally change the nature of phase transitions in spin models.
• The discovered explosive transitions and hysteresis offer new insights into complex system dynamics.
• Mean-field theory provides an analytical framework to understand these novel transition properties.