Critical behavior of a spring-block model for magnetization

The critical behavior of a one-dimensional spring-block model aimed to describe magnetization phenomena is studied by Monte-Carlo type computer simulations. The introduced model resembles the classical Burridge-Knopoff type models where the blocks represent the Bloch-walls that separate inversely oriented magnetic domains, and springs correspond to the magnetized regions. Disorder is introduced through randomly distributed pinning centers along the sample and the magnetization process is modeled through a relaxational dynamics. The shape of the hysteresis loops and the distribution of avalanche sizes are studied (jumps in magnetization) for different disorder values. As a function of the amount of disorder in the system, in agreement with previously introduced magnetization models, the subcritical, critical and supercritical regions are identified. The results indicate that for a critical amount of disorder the introduced model exhibits critical behavior characterized by power-law distribution of the avalanche sizes. An estimation of the critical exponent is given.