Exploring time-extended complexity measures in magnetic systems

Abstract: Complexity, a fundamental concept in physics, encompasses phenomena spanning atomic to cosmic scales. The natural emergence of complexity can be explained by self-organized criticality. In this work, two complexity measures in magnetic systems are explored. The multiscale structural complexity (MSC) and spin temperature both capture complexity but are fundamentally different in nature and hence behave differently when subject to various temperature profiles. The MSC is extended to incorporate time correlations and compared to the time-averaged static MSC for examining spin glasses and bcc Fe at different temperatures. The spin glass transition temperature is determined with an accuracy of 1 K using the time-extended MSC, outperforming similar estimates based on the heat capacity in terms of accuracy, computational cost, and efficiency. Future work includes the optimization of coarse-graining scales in spin glasses, the investigation of transient magnetization dynamics, and the influence and loss of information of averaging magnetic unit cells before computing complexities.