Abstract
We study avalanches along the hysteresis loop of long-range interacting spin glasses with continuous symmetry, which serves as a toy model of granular superconductors with long-range and frustrated Josephson couplings. We identify sudden jumps in the configurations of the phases as an external field is increased. They are initiated by the softest mode of the inverse susceptibility matrix becoming unstable, which induces an avalanche of phase updates (or spin alignments). We analyze the statistics of these events and study the correlation between the nonlinear avalanches and the soft mode that initiates them. We find that the avalanches follow the directions of a small fraction of the softest modes of the inverse susceptibility matrix, similarly as was found in avalanches in jammed systems. In contrast to the similar Ising spin glass (Sherrington-Kirkpatrick) studied previously, we find that avalanches are not distributed with a scale-free power law but rather have a typical size which scales with the system size. We also observe that the Hessians of the spin-glass minima are not part of standard random matrix ensembles as the lowest eigenvector has a fractal support.
5 More- Received 26 June 2014
DOI:https://doi.org/10.1103/PhysRevE.90.042103
©2014 American Physical Society