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

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 (H)over dot 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 (H)over dot that are fixed as well, to elucidate the differences in the response. root Specifically, we compare three different modes of ramping (H(H)over dot = c/N, (H)over dot = c/root N , and (H)over dot = 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.