We demonstrate that a two-dimensional finite and periodic array of Ising spins coupled via RKKY-like exchange can exhibit tunable magnetic states ranging from three distinct magnetic regimes: (1) a conventional ferromagnetic regime, (2) a glass-like regime, and (3) a new multi-well regime. These magnetic regimes can be tuned by one gate-like parameter, namely the ratio between the lattice constant and the oscillating interaction wavelength. We characterize the various magnetic regimes, quantifying the distribution of low energy states, aging relaxation dynamics, and scaling behavior. The glassy and multi-well behavior results from the competing character of the oscillating long-range exchange interactions. The multi-well structure features multiple attractors, each with a sizable basin of attraction. This may open the possible application of such atomic arrays as associative memories.
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