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The d = 1, O(N ≥ 3) Rotor Models

Subir Sachdev A

Published Jan 13, 2000• 0 citations

Abstract

As we noted in the preface, this and the following chapter are at a more advanced level, and some readers may wish to skip ahead to Chapter 8. In Chapter 5 we studied the O( N ) quantum rotor model in the large- N limit for a number of values of the spatial dimensionality, including d = 1. We noted that the results provided an adequate description of the static properties in d = 1 for N ≥ 3. This will be justified in the present chapter where we will obtain a number of exact results for the same static observables. We also noted that the large- N limit did a very poor job of describing dynamical properties at nonzero temperatures. This will be repaired in this chapter by simple physical arguments that lead to a fairly complete (and believed exact) description of the long-time behavior. Some of the discussion in this chapter will be specialized to the O( N = 3) model, which is also the case of greatest physical importance; the properties of the O( N > 3) models are very similar, and many of our results will be quoted for general N . Of the remaining cases, the d = 1, N = 1 model has been already considered in Chapter 4, and study of the d = 1, N = 2 model is postponed to Section 14.3. The physical picture of the T = 0, N = 3 state that emerged in Chapter 5 was very simple.

DOI: 10.1017/cbo9780511622540.007

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