Gauged O(n) spin models in one dimension - Hasenbusch, Martin; Horgan, Ron R. (Physical review. D, Particles, fields, gravitation, and cosmology, 1999)
We consider a gauged O(n) spin model, n>~2, in one dimension which contains both the pure O(n) and RPn−1 spin models and which 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 it has been suggested that, for n>2, three distinct universality classes exist and that RPn−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 Ising model which allows a simple derivation of the complete mass spectrum that scales in the continuum limit. We demonstrate that there are only two universality 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 that it arises from the direct sum of the O(n) and Ising models.