  We study the correlation function of middle spins, i. e. of spins on
intermediate sites between two adjacent parallel lattice axes, of the spatially
anisotropic Ising antiferromagnet on the kagome lattice. It is given rigorously
by a Toeplitz determinant. The large-distance behaviour of this correlation
function is obtained by analytic methods. For shorter distances we evaluate the
Toeplitz determinant numerically. The correlation function is found to vanish
exactly on a line J_d(T) in the T-J (temperature vs. coupling constant) phase
diagram. This disorder line divides the phase diagram into two regions. For J
less than J_d(T) the correlations display the features of an unfrustrated
two-dimensional Ising magnet, whereas for J greater than J_d(T) the
correlations between the middle spins are seen to be strongly influenced by the
short-range antiferromagnetic order that prevails among the spins of the
adjacent lattice axes. While for J less than J_d(T) there is a region with
ferrimagnetic long-range order, the model remains disordered for J greater than
J_d(T) down to T=0.
