Large fluctuations of local magnetizations in one-dimensional magnets

Large spatial fluctuations of local magnetizations in the one-dimensional Ising and the spin chains are studied from the viewpoint of the fluctuation spectrum, and the generalized spatial correlations are also calculated. This is based on the fact that large fluctuation characteristics of local magnetizations without external field are determined by small fluctuations of the system under external field. It is shown that at low temperatures the functions relevant to the large fluctuations satisfy scaling laws.