Exact Solutions for Correlations in the Kagomé Ising Antiferromagnet

Abstract

The kagomé Ising antiferromagnet is highly frustrated with its pair correlation decaying exponentially at large distance for all temperatures including absolute zero. Hence, the spin system does not support long-range orderings and is devoid of any phase transition. One proves, via local star-triangle and decoration-decimation transformations, that correlations in the kagomé Ising antiferromagnet at arbitrary temperatures 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 all present kagomé Ising correlations upon an associated 9-site cluster. Examples of resulting exact solutions for pair and multisite correlations in the kagomé Ising antiferromagnet are presented at all temperatures. Applications include joint configuration probabilities, thermodynamic response functions such as the specific heat and the initial perpendicular susceptibility, and the inelastic neutron scattering function.