Avalanches and hysteresis in frustrated superconductors and XY-spin-glasses

Abstract

We study avalanches along the hysteresis loop of long-range interacting spin-glasses with continuous XY-symmetry - which serves as a toy model of granular superconductors with long-range and frustrated Josephson couplings. We identify sudden jumps in the $T=0$ configurations of the XY-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 non-linear 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.

17 pages, 12 figures

References in corpus (6)

• Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition
• Exactly solvable model of avalanches dynamics for Barkhausen crackling noise
• Theory of quantum metal to superconductor transitions in highly conducting systems
• Heterogeneous Dynamics, Marginal Stability and Soft Modes in Hard Sphere Glasses
• Large-scale Monte Carlo simulations of the isotropic three-dimensional Heisenberg spin glass
• Marginal States in Mean Field Glasses

Cited by in corpus (4)

• Marginal Stability in Structural, Spin and Electron Glasses
• The metastable minima of the Heisenberg spin glass in a random magnetic field
• Study of the de Almeida-Thouless (AT) line in the one-dimensional diluted power-law XY spin glass
• Exact numerical solution of the fully-connected classical and quantum Heisenberg spin glass