Continuum Limit and Improved Action in Lattice Theories. 2. O(N) Nonlinear Sigma Model in Perturbation Theory

The method of paper (I) of this series is applied to the O(N) non-linear sigma model. Due to the use of non-manifestly invariant perturbation theory the improvement part of the action, computed explicitly to one-loop order, is not manifestly O(N) invariant. It can be brought into manifestly O(N) invariant form by use of linear identities among dimension-four operators, which follow from the field equations of the unimproved action. The adequacy of the resulting two-parameter family of manifestly O(N) invariant improved actions is verified to one-loop order.

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