Book contents
- Frontmatter
- Contents
- Foreword and general introduction
- 1 Some basic notions of classical and quantum statistical physics
- 2 General theory of phase transitions
- 3 Bose and Fermi statistics
- 4 Phonons in crystals
- 5 General Bose systems; Bose condensation
- 6 Magnetism
- 7 Electrons in metals
- 8 Interacting electrons. Green functions and Feynman diagrams (methods of field theory in many-particle physics)
- 9 Electrons with Coulomb interaction
- 10 Fermi-liquid theory and its possible generalizations
- 11 Instabilities and phase transitions in electronic systems
- 12 Strongly correlated electrons
- 13 Magnetic impurities in metals, Kondo effect, heavy fermions and mixed valence
- Bibliography
- Index
2 - General theory of phase transitions
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Foreword and general introduction
- 1 Some basic notions of classical and quantum statistical physics
- 2 General theory of phase transitions
- 3 Bose and Fermi statistics
- 4 Phonons in crystals
- 5 General Bose systems; Bose condensation
- 6 Magnetism
- 7 Electrons in metals
- 8 Interacting electrons. Green functions and Feynman diagrams (methods of field theory in many-particle physics)
- 9 Electrons with Coulomb interaction
- 10 Fermi-liquid theory and its possible generalizations
- 11 Instabilities and phase transitions in electronic systems
- 12 Strongly correlated electrons
- 13 Magnetic impurities in metals, Kondo effect, heavy fermions and mixed valence
- Bibliography
- Index
Summary
The state of different condensed matter systems is characrerized by different quantities: density, symmetry of a crystal, magnetization, electric polarization, etc. Many such states can have a certain ordering. Different types of ordering can be characterized by order parameters.
Examples of order parameters are, for instance: for ferromagnets – the magnetization M; for ferroelectrics – the polarization P; for structural phase transitions – the distortion uαβ, etc. Typically the system is disordered at high temperatures, and certain types of ordering may appear with decreasing temperature. This is clear already from the general expressions for thermodynamic functions, see Chapter 1: at finite temperatures the state of the system is chosen by the condition of the minimum of the corresponding thermodynamic potential, the Helmholtz free energy (1.8) or the Gibbs free energy (1.10), and from those expressions it is clear that with increasing temperature it is favourable to have the highest entropy possible, i.e. a disordered state. But some types of ordering are usually established at lower temperatures, where the entropy does not play such an important role, and the minimum of the energy is reached by establishing that ordering.
The general order parameter η depends on temperature, and in principle also on other external parameters – pressure, magnetic field, etc. Typical cases of the dependence of the order parameter on temperature are shown in Fig. 2.1.
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- Basic Aspects of the Quantum Theory of SolidsOrder and Elementary Excitations, pp. 6 - 30Publisher: Cambridge University PressPrint publication year: 2010
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