Sometimes a great motion: creating critical processes using parallel spin flips in marginally stable systems

We study the dynamics of marginally stable systems under different driving mechanisms. A typical example is the mean-field Sherrington-Kirkpatrick spin glass (SK) at T=0. The local energy minima reached, either after a thermal quench or when spins σ_i are entrained with a slowly ramping external field H_ext, exhibit a wide distribution, P(h), of their local fields h_i with whom each spin aligns. These local fields are a measure of their stability. In particular, in SK, P(h) forms a pseudo-gap, i.e., there are near-zero local fields such that P(h) ∼ h for h → 0. Thus, even minute environmental changes (like, in H_ext) will destabilize numerous spins, and SK has been shown to undergo a critical avalanche process in response. Here, we will drive the dynamics not by coupling to the spins with the external field H_ext impinging on their local fields h_i , but rather by affecting their individual stability (or “fitness”), λ_i = σ_i h_i , directly, whereas H_ext ≡ 0. Albeit somewhat unphysical, this alternate way of driving also evolves into a critical process with an interesting avalanche dynamics, which has proven to be an efficient way to find global energy minima for SK, thus, solving an NP-hard optimization problem. We will also discuss the effect of this form of driving for spin glasses without a pseudo-gap, such as the Edwards-Anderson lattice spin glass and other sparse networks.