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

TL;DR

This paper introduces a non-equilibrium, memory-based dynamic approach to simulate spin glasses, enabling more efficient exploration of their complex energy landscapes by promoting critical clusters and overcoming metastability.

Contribution

It presents a novel memory-driven dynamic method for simulating spin glasses, improving exploration efficiency over traditional cluster algorithms.

Findings

Memory dynamically promotes critical spin clusters.

Facilitates efficient exploration of low-temperature phases.

Self-organizing behavior enhances simulation performance.

Abstract

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