Hysteretic response to different modes of ramping an external field in sparse and dense Ising spin glasses

Mahajabin Rahman and Stefan Boettcher

Physica A: Statistical Mechanics and its Applications, 2024, vol. 653, issue C

Abstract: We consider the hysteretic behavior of Ising spin glasses at T=0 for various modes of driving. Previous studies mostly focused on an infinitely slow speed Ḣ by which the external field H was ramped to trigger avalanches of spin flips by starting with destabilizing a single spin while few have focused on the effect of different driving methods. First, we show that this conventional protocol imposes a system size dependence. Then, we numerically analyze the response of Ising spin glasses at rates Ḣ that are fixed as well, to elucidate the differences in the response. Specifically, we compare three different modes of ramping (Ḣ=c/N, Ḣ=c/N, and Ḣ=c for constant c) for two types of spin glass systems of size N, representing dense networks by the Sherrington–Kirkpatrick model and sparse networks by the lattice spin glass in d=3 dimensions known as the Edwards Anderson model. Depending on the mode of ramping, we find that the response of each system, in form of spin-flip avalanches and other observables, can vary considerably. In particular, in the N-independent mode applied to the lattice spin glass, which is closest to experimental reality, we observe a percolation transition with a broad avalanche distribution between phases of localized and system-spanning responses. We explore implications for combinatorial optimization problems pertaining to sparse systems.

Keywords: Ising spin glasses; Hysteresis; Percolation; Optimization; Self-organized criticality; Avalanches (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:653:y:2024:i:c:s037843712400579x

DOI: 10.1016/j.physa.2024.130070

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