Avalanches in complex spin networks

TL;DR

This paper studies how the structure of complex spin networks influences magnetization reversal and avalanche phenomena, revealing power-law distributions of avalanche sizes related to network topology.

Contribution

It provides a detailed analysis of magnetization avalanches and hysteresis in complex spin networks, linking their properties to network inhomogeneity and topology.

Findings

Avalanche size distribution follows a power-law for small sizes.

Scale-free networks show increasing power-law exponent with connectivity.

Exponential networks have a consistent exponent near 1.0.

Abstract

We investigate the magnetization reversal processes on classes of complex spin networks with antiferromagnetic interaction along the network links. With slow field ramping the hysteresis loop and avalanches of spin flips occur due to topological inhomogeneity of the network, even without any disorder of the magnetic interaction [B. Tadic, et al., Phys. Rev. Lett. 94 (2005) 137204]. Here we study in detail properties of the magnetization avalanches, hysteresis curves and density of domain walls and show how they can be related to the structural inhomogeneity of the network. The probability distribution of the avalanche size, N_s(s), displays the power-law behaviour for small s, i.e. N_s(s)\propto s^{-\alpha}. For the scale-free networks, grown with preferential attachment, \alpha increases with the connectivity parameter M from 1.38 for M=1 (trees) to 1.52 for M=25. For the exponential networks, \alpha is close to 1.0 in the whole range of M.