Gauged O(n) spin models in one dimension - art. no. 037503.

We consider a gauged O(n) spin model, n greater than or equal to 2, in one dimension which contains both the pure O(n) and Rp(n-1) spin models and whi ch interpolates between them. Various formulations of this theory are given , one of which shows that it belongs to a general set of models for which i t has been suggested that, for n>2, three distinct universality classes exi st and that Rp(n-1) and O(n) belong to different classes. We show that our model is equivalent to the non-interacting sum of an O(n) model and the Isi ng model which allows a simple derivation of the complete mass spectrum tha t scales in the continuum limit. We demonstrate that there are only two uni versality classes, one of which contains the O(n) and RPn-1 models and the other which has a tunable parameter, but which is degenerate in the sense t hat it arises from the direct sum of the O(n) and Ising models. [S0556-2X21 (99)06213-X].