Correlations in Ising chains with nonintegrable interactions.

Two-spin correlations generated by interactions which decay with distance r as r−1−σ with −1 < σ < 0 are calculated for periodic Ising chains of length L. Mean-field theory indicates that the correlations, C(r, L), diminish in the thermodynamic limit L → ∞, but they contain a singular structure for r/L → 0 which can be observed by introducing magnified correlations, LC(r, L)−∑r C(r, L). The magnified correlations are shown to have a scaling form Φ(r/L) and the singular structure of Φ(x) for x → 0 is found to be the same at all temperatures including the critical point. These conclusions are supported by the results of Monte Carlo simulations for systems with σ = −0.50 and −0.25 both at the critical temperature T = Tc and at T = 2Tc. PACS numbers: 05.50.+q, 05.70.Ln, 64.60Cn