Correlations in the Ising antiferromagnet on the anisotropic kagome lattice

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 Jd(T) in the T − J (temperature versus coupling constant) phase diagram. This disorder line divides the phase diagram into two regions. For J Jd(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 Jd(T) down to T = 0.