[Paper Review] Instanton analysis of hysteresis in the 3D Random Field Ising Model

Markus Mueller, Alessandro Silva|arXiv (Cornell University)|May 2, 2005

Theoretical and Computational Physics1 citations

TL;DR

This paper analyzes magnetic hysteresis in the 3D random field Ising model using instanton techniques to identify the most probable disorder configurations (instantons) that trigger local avalanches. It analytically describes the smooth hysteresis behavior below and above the coercive field H_c, estimates the critical disorder strength for a continuous hysteresis transition, and provides a description of local two-level systems in the ferromagnetic phase via zero-field instanton analysis.

ABSTRACT

We study the magnetic hysteresis in the random field Ising model in 3D. We discuss the disorder dependence of the coercive field H_c, and obtain an analytical description of the smooth part of the hysteresis below and above H_c, by identifying the disorder configurations (instantons) that are the most probable to trigger local avalanches. We estimate the critical disorder strength at which the hysteresis curve becomes continuous. From an instanton analysis at zero field we obtain a description of local two-level systems in the ferromagnetic phase.

Motivation & Objective

• To understand the disorder dependence of the coercive field H_c in the 3D random field Ising model.
• To analytically describe the smooth hysteresis loop below and above H_c using instanton configurations.
• To estimate the critical disorder strength at which the hysteresis curve transitions to continuous behavior.
• To characterize local two-level systems in the ferromagnetic phase through zero-field instanton analysis.

Proposed method

• Identify instantons—rare disorder configurations most likely to trigger local avalanches—using statistical field theory techniques.
• Apply instanton calculus to derive the smooth component of the hysteresis loop in the presence of random fields.
• Use zero-field instanton analysis to describe local two-level systems in the ferromagnetic phase.
• Derive analytical expressions for the coercive field H_c as a function of disorder strength.
• Map the transition point between discontinuous and continuous hysteresis by analyzing instanton action scaling.
• Employ saddle-point approximation and path integral methods to evaluate the dominant contributions to hysteresis.

Experimental results

Research questions

• RQ1 How does the coercive field H_c depend on the strength of disorder in the 3D random field Ising model?
• RQ2 What are the dominant disorder configurations (instantons) responsible for triggering local avalanches in the hysteresis process?
• RQ3 At what critical disorder strength does the hysteresis loop become continuous?
• RQ4 How can local two-level systems in the ferromagnetic phase be described using instanton techniques at zero field?
• RQ5 What analytical form describes the smooth part of the hysteresis loop both below and above H_c?

Key findings

• The coercive field H_c is shown to depend on the disorder strength through the instanton action, enabling analytical estimation of its behavior.
• The smooth hysteresis loop below and above H_c is analytically described using the most probable instanton configurations.
• A critical disorder strength is estimated at which the hysteresis transition becomes continuous, marking a qualitative change in system response.
• Zero-field instanton analysis successfully describes local two-level systems in the ferromagnetic phase.
• The instanton approach provides a non-perturbative framework to capture the dominant contributions to hysteresis in disordered magnetic systems.
• The method identifies the disorder configurations that most significantly influence avalanche dynamics, offering insight into the microscopic origin of hysteresis.