Abstract
We study the correlation function of middle spins, i.e. of spins on intermediatesites between two adjacent parallel lattice axes, of the spatially anisotropic Isingantiferromagnet on the kagome lattice. It is given rigorously by a Toeplitzdeterminant. The large-distance behaviour of this correlation function is obtained byanalytic methods. For shorter distances we evaluate the Toeplitz determinantnumerically. The correlation function is found to vanish exactly on a lineJd(T) inthe T − J (temperature versus coupling constant) phase diagram. Thisdisorder line divides the phase diagram into two regions. ForJ < Jd(T) the correlations display the features of an unfrustrated two-dimensional Ising magnet, whereas forJ > Jd(T) the correlations between the middle spins are seen to be strongly influenced by the short-rangeantiferromagnetic order that prevails among the spins of the adjacent lattice axes. While forJ < Jd(T) there is a region with ferrimagnetic long-range order, the model remains disordered forJ > Jd(T) downto T = 0.
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