EXACT-SOLUTIONS FOR CORRELATIONS IN THE KAGOME ISING ANTIFERROMAGNET

The kagome Ising antiferromagnet is highly frustrated with its pair co rrelation decaying exponentially at large distance for all temperature s including absolute zero. Hence, the spin system does not support lon g-range orderings and is devoid of any phase transition. One proves, v ia local star-triangle and decoration-decimation transformations, that correlations in the kagome Ising antiferromagnet at arbitrary tempera tures can be represented as linear combinations of correlations in the honeycomb Ising ferromagnet at high temperatures (disordered region). Existent knowledge of all honeycomb Ising correlations upon a select (spatially compact) 10-site cluster is thus sufficient to determine al l present kagome Ising correlations upon an associated 9-site cluster. Examples of resulting exact solutions for pair and multisite correlat ions in the kagome Ising antiferromagnet are presented at all temperat ures. Applications include joint configuration probabilities, thermody namic response functions such as the specific heat and the initial per pendicular susceptibility, and the inelastic neutron scattering functi on.