Book contents
- Frontmatter
- Contents
- From the Preface to the first edition
- Preface to the second edition
- Part I Introduction
- Part II A first course
- Part III Nonzero temperatures
- 10 The Ising chain in a transverse field
- 11 Quantum rotor models: large-N limit
- 12 The d = 1, O(N ≥ 3) rotor models
- 13 The d = 2, 0(N ≥ 3) rotor models
- 14 Physics close to and above the upper-critical dimension
- 15 Transport in d = 2
- Part IV Other models
- References
- Index
10 - The Ising chain in a transverse field
from Part III - Nonzero temperatures
Published online by Cambridge University Press: 16 May 2011
- Frontmatter
- Contents
- From the Preface to the first edition
- Preface to the second edition
- Part I Introduction
- Part II A first course
- Part III Nonzero temperatures
- 10 The Ising chain in a transverse field
- 11 Quantum rotor models: large-N limit
- 12 The d = 1, O(N ≥ 3) rotor models
- 13 The d = 2, 0(N ≥ 3) rotor models
- 14 Physics close to and above the upper-critical dimension
- 15 Transport in d = 2
- Part IV Other models
- References
- Index
Summary
Part II analyzed the properties of quantum Ising and rotor models in some detail at T = 0. We related the quantum phase transitions in these models to the N-component relativistic field theory (2.11), and used it to understand the critical properties.
The purpose of Part III is to extend this understanding to T > 0. We will demonstrate that the T = 0 quantum critical point controls a wide “quantum critical” region at T > 0, as illustrated in Fig. 1.2. We are especially interested in dynamic properties in this region: an interesting feature is that many “friction” coefficients are universal and depend only on fundamental constants of nature. We also explore the other regions of the phase diagrams in Fig. 1.2, including behavior in the vicinity of the phase transition at T > 0.
We begin this chapter by extending results of the d = 1 quantum Ising model of Chapter 5 to T > 0. This model does not have any phase transition at any T > 0, and so the crossover structure of the phase diagram is in the class in Fig. 1.2a. Phase transitions at T > 0 appear in models to be studied in the following chapter.
- Type
- Chapter
- Information
- Quantum Phase Transitions , pp. 135 - 170Publisher: Cambridge University PressPrint publication year: 2011