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Despite their simple formulation, short range classical antiferromagneticIsing models on frustrated lattices give rise to exotic phases of matter, inparticular due to their macroscopic ground state degeneracy. Recent experimentson artificial spin systems comprising arrays of chirally coupled nanomagnetsprovide a significant strengthening of the nearest neighbour couplings comparedto systems with dipolar-coupled nanomagnets. This opens the way to designartificial spin systems emulating Ising models with nearest neighbourcouplings. In this paper, we compare the results of an extensive investigationwith tensor network and Monte Carlo simulations of the nearest- andfurther-neighbour ($J_1-J_2-J_{3||}$) kagome Ising antiferromagnet with theexperimental spin-spin correlations of a kagome lattice of chirally couplednanomagnets. Even though the ratios between the further neighbour couplings andthe nearest neighbour coupling estimated from micromagnetic simulations aremuch smaller than for dipolar-coupled nanomagnets, we show that they still playan essential role in the selection of the correlations.

Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small further neighbour couplings