Hard-spin mean-field theory: A systematic derivation and exact correlations in one dimension

Hard-spin mean-field theory is an improved mean-held approach which has proven to give accurate results, especially for frustrated spin systems, with relatively Little computational effort. In this. work. the previous phenomenological derivation is supplanted by a systematic and generic derivation that opens the possibility for systematic improvements, especially for the calculation of long-range correlation functions. A first level of improvement suffices to recover the exact long-range values of the correlation functions in one dimension.