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

TL;DR

This paper investigates avalanches and hysteresis in a model of frustrated superconductors with XY spins, revealing that avalanches are initiated by soft modes and have typical sizes, contrasting with scale-free distributions in similar models.

Contribution

It introduces a detailed analysis of avalanche dynamics in XY-spin-glasses, highlighting the role of soft modes and the non-scale-free nature of avalanches, differing from Ising models.

Findings

Avalanches are triggered by softest modes of the inverse susceptibility matrix.

Avalanche sizes scale with system size, not following a power-law distribution.

Hessian eigenvectors at minima have fractal support, differing from standard random matrix ensembles.

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.