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Spin glasses are notoriously difficult to study both analytically andnumerically due to the presence of frustration and metastability. Their highlynon-convex landscapes require collective updates to explore efficiently.Currently, most state-of-the-art algorithms rely on stochastic spin clusters toperform non-local updates, but such "cluster algorithms" lack generalefficiency. Here, we introduce a non-equilibrium approach for simulating spinglasses based on classical dynamics with memory. By simulating various classesof 3d spin glasses (Edwards-Anderson, partially-frustrated, andfully-frustrated models), we find that memory dynamically promotes criticalspin clusters during time evolution, in a self-organizing manner. Thisfacilitates an efficient exploration of the low-temperature phases of spinglasses.

Non-equilibrium criticality and efficient exploration of glassy landscapes with memory dynamics