  Despite their simple formulation, short range classical antiferromagnetic
Ising models on frustrated lattices give rise to exotic phases of matter, in
particular due to their macroscopic ground state degeneracy. Recent experiments
on new artificial spin systems comprising arrays of chirally coupled
nanomagnets provide a significant strengthening of the nearest neighbour
couplings compared to systems with dipolar-coupled nanomagnets. This opens the
way to design artificial spin systems emulating Ising models with nearest
neighbour couplings. In this paper, we compare the results of an extensive
investigation with tensor network and Monte Carlo simulations of the nearest-
and further-neighbour ($J_1-J_2-J_{3||}$) kagome Ising antiferromagnet with the
experimental spin-spin correlations of a kagome lattice of chirally coupled
nanomagnets. Even though the ratios between the further neighbour couplings and
the nearest neighbour coupling estimated from micromagnetic simulations are
much smaller than for dipolar-coupled nanomagnets, we show that they still play
an essential role in the selection of the correlations.
