Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Part I Introduction
- Part II Quantum Ising and Rotor Models
- 4 The Ising Chain in a Transverse Field
- 5 Quantum Rotor Models: Large-N Limit
- 6 The d = 1, O(N ≥ 3) Rotor Models
- 7 The d = 2, O(N ≥ 3) Rotor Models
- 8 Physics Close to and above the Upper-Critical Dimension
- 9 Transport in d = 2
- Part III Other Models
- References
- Index
9 - Transport in d = 2
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Part I Introduction
- Part II Quantum Ising and Rotor Models
- 4 The Ising Chain in a Transverse Field
- 5 Quantum Rotor Models: Large-N Limit
- 6 The d = 1, O(N ≥ 3) Rotor Models
- 7 The d = 2, O(N ≥ 3) Rotor Models
- 8 Physics Close to and above the Upper-Critical Dimension
- 9 Transport in d = 2
- Part III Other Models
- References
- Index
Summary
We considered time-dependent correlations of the conserved angular momentum, L(x, t), of the O(3) quantum rotor model in d = 1 in Chapter 6. We found, using effective semiclassical models, that the dynamic fluctuations of L(x, t) were characterized by a diffusive form (see (6.26)) at long times and distances, and we were able to obtain values for the spin diffusion constant Ds at low T and high T (see Fig. 6.5). The purpose of this chapter is to study the analogous correlations in d = 2 for N ≥ 2; the case N = 1 has no conserved angular momentum, and so there is no possibility of diffusive spin correlations. Rather than thinking about fluctuations of the conserved angular momentum in equilibrium, we shall find it more convenient here to consider instead the response to an external space and time dependent “magnetic” field H(x, t) and to examine how the system transports the conserved angular momentum under its influence.
In principle, it is possible to address these issues in the high-T region using the nonlinear classical wave problem developed in Section 8.3 in the context of the ∈ = 3 − d expansion. However, an attempt to do this quickly shows that the correlators of L contain ultraviolet divergences when evaluated in the effective classical theory.
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- Chapter
- Information
- Quantum Phase Transitions , pp. 168 - 190Publisher: Cambridge University PressPrint publication year: 2000