The continuum limit of one-dimensional non-linear models

Group invariant expectation values for lattice non-linear vector models [O(N) and CPN−1] in one dimension with a general local action may be expressed as explicit functions of the single-link model expectation values. The value of all these averages at the fixed point of the renormalization group can be determined exactly, in such a way that the continuum expectation values are generated. The large N limit and the reconstruction of the fixed point lattice action are discussed.