Stochastic model of hysteresis

Area of Science:

• Statistical Physics
• Probability Theory
• Materials Science

Background:

• Hysteresis is a critical phenomenon in various physical systems, often modeled by the Preisach model.
• Understanding the underlying stochastic processes governing transitions is essential for accurate hysteresis modeling.
• Existing models may not fully capture the nuances of accommodation and memory effects in hysteresis loops.

Purpose of the Study:

• To develop a new probability theory-based model for hysteresis, distinct from the Preisach model.
• To analyze the stochastic evolution of systems with two-state particles under external parameter variations.
• To explain the accommodation process and memory properties of hysteresis loops.

Main Methods:

• Modeling hysteresis using probability theory and abstract particles with two states (+1 and -1).
• Defining transitions between states using random variables for 'up' and 'down' switching.
• Analyzing the probability distribution and expectation values to determine hysteresis curves.

Main Results:

• Reversal points act as Markov points governing stochastic evolution.
• Hysteresis loop branches converge to limit curves, explaining the accommodation process.
• The model shows non-zero reversal point susceptibilities and approximates the Rayleigh law for small parameter variations.

Conclusions:

• The proposed stochastic model provides a new framework for understanding and calculating hysteresis.
• It offers a clear explanation for the accommodation process and return-point memory effects.
• The model aligns well with experimental observations and aids in estimating switching field distributions.