Correlations in Ising chains with nonintegrable interactions

Two-spin correlations generated by interactions that decay with distance r as r(-1-sigma) with -1 < sigma < 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 --> infinity, but that they contain a singular structure for r/L --> 0 that can be observed by introducing magnified correlations LC(r,L)-Sigma(r) C(r, L). The magnified correlations are-shown to have a scaling form phi(r/L))and the singular structure of phi(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 sigma = -0.50 and -0.25 both at the critical temperature T = T-c and at T = 2T(c).