Optimization and self-organized criticality in a magnetic system

TL;DR

This paper introduces a Bak-Sneppen based optimization method for magnetic systems, demonstrating self-organized criticality and comparing its efficiency with extremal optimization using the chiral clock model.

Contribution

It presents a novel application of Bak-Sneppen dynamics as an optimization technique for magnetic systems and analyzes its critical behavior and efficiency.

Findings

Bak-Sneppen dynamics shows self-organized criticality with power-law correlations.

Extremal optimization exhibits non-critical behavior with exponential avalanche decay.

The two methods differ in their ability to find the ground state of the system.

Abstract

We propose a kind of Bak-Sneppen dynamics as a general optimization technique to treat magnetic systems. The resulting dynamics shows self-organized criticality with power law scaling of the spatial and temporal correlations. An alternative method of the extremal optimization is also analyzed here. We provided a numerical confirmation that, for any possible value of its free parameter $\tau$, the extremal optimization dynamics exhibits a non-critical behavior with an infinite spatial range and exponential decay of the avalanches. Using the chiral clock model as our test system, we compare the efficiency of the two dynamics with regard to their abilities to find the system's ground state.