  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 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.
