Finite-Temperature Avalanches in 2D Disordered Ising Models

Abstract

We study the qualitative and quantitative properties of the Barkhausen noise emerging at finite temperatures in random Ising models. The random-bond Ising Model is studied with a Wolff cluster Monte-Carlo algorithm to monitor the avalanches generated by an external driving magnetic field. Satisfactory power-law distributions are found which expand over five decades, with a temperature-dependent critical exponent which matches the existing experimental measurements. We also focus on a Ising system in which a finite fraction of defects is quenched. Also the presence of defects proves able to induce a critical response to a slowly oscillating magnetic field, though in this case the critical exponent associated with the distributions obtained with different defect fractions and temperatures seems to belong to the same universality class, with a critical exponent close to 1.

Dynamic Phase Transition in 2D Ising Systems: Effect of Anisotropy and Defects

“…In this way, frozen domains contribute to identifying the ordered phase, independently of their sign. For homogenous systems, locating the phase transition through either the order parameter (12) or (10) provides the same results.…”

“…The findings reveal that only data for L ≲ 30 exhibit weak size dependence. The remarkable absence of finite-size effects is most likely to be associated with the definition of the dynamic order parameter (12). This formulation specifically measures the extent to which sites adhere to external field oscillations and how many remain stuck in a magnetized state, irrespective of the sign of the trapping magnetized phase.…”

“…Magnetic systems, particularly the Ising spin model, provide a simple yet highly fruitful terrain for studying and understanding different dynamic phenomena [6,7]. The Barkhausen noise [8][9][10][11][12] is a paradigmatic example of bursty behavior emerging from a slow driving, and nucleation phenomena can be explored to understand how first-order transitions can be induced and driven in bistable systems [13][14][15][16].…”