The Pseudo-Spin Method in Magnetism and Ferroelectricity

The Pseudo-Spin Method in Magnetism and Ferroelectricity deals with the pseudo-spin method in magnetism and ferroelectricity, with emphasis on three important ordered systems: ferromagnets, antiferromagnets, and hydrogen-bonded ferroelectrics. Each system is analyzed in three important temperature regions: low temperatures, the critical region, and high temperatures. The presented mathematical method is predominantly analytical in the sense that all crucial physical quantities are expressed in terms of temperature or the reciprocal lattice vectors.

Comprised of four chapters, this volume begins with an introduction to Basic concepts in lattice dynamics, touching on topics such as symmetry groups, light scattering, and the spectrum of ionic crystals. The discussion then turns to phase transitions and covers magnetism, ferroelectricity, and the Ising model with a transverse field. Magnetic elementary excitations are then considered, paying particular attention to the second quantization method; the exchange interaction; the Heisenberg ferromagnet in a boson representation; and high-temperature static susceptibility. The final chapter is devoted to the Green functions and their perturbation expansion; ferromagnetism at low temperatures; antiferromagnetism and ferroelectric modes; and high-temperature dielectric susceptibilities.

This book will be of interest to physicists as well as students and researchers in physics.

Contenu

Acknowledgments
Introduction
Chapter 1. Lattice Dynamics
1.1 Basic Concepts in Symmetry Groups
1.2. Light Scattering
1.3. Selection Rules for the Translation and Tensor Representations
1.4. The Reciprocal Lattice
1.5. Basic Concepts in Lattice Dynamics
1.6. The Spectrum of Ionic Crystals
1.7. Diffuse Modes
1.8. The Normal Hydrogen Vibration Modes, I
1.9. The Normal Hydrogen Vibration Modes, II
References
Chapter 2. Phase Transitions
2.1. Magnetism, I
2.2. Magnetism, II
2.3. The Ising Model with a Parallel Field
2.4. Ferroelectricity
2.5. The Ising Model with a Transverse Field: General Theory
2.6. The Ising Model with a Transverse Field: Molecular-Field Approximation
2.7. The Critical-Point Exponents
References
Chapter 3. Magnetic Elementary Excitations
3.1. The Second Quantization Method
3-2. The Exchange Interaction
3.3. The Spin Variables through the Second Quantization Method
3.4. The Heisenberg Ferromagnet in a Boson Representation
3.5. The Spontaneous Magnetization and Specific Heat
3.6. A Review of Genuine Papers Devoted to Spin Waves
3.7. The Dispersion Law for Antiferromagnets with a Double Heisenberg Exchange Interaction
3.8. The High-Temperature Static Susceptibility, I
3.9. The High-Temperature Static Susceptibility, II
References
Chapter 4. The Use of Green Functions
4.1. Basic Definitions
4.2. Perturbation Expansion for the Green Functions
4.3. Ferromagnetism at Low Temperatures
4.4. The Kinematical Interaction
4.5. Antiferromagnetism, I
4.6. Antiferromagnetism, II
4.7. Experimental Evidence
4.8. The Ferroelectric Modes
4.9. High-Temperature Dielectric Susceptibilities
References
Appendix A. Cubic Lattices
Appendix B. A Method used to Separate the Proton Coordinates from those of Heavy Clusters
Appendix C. The Use of Gamma and Zeta Functions
Appendix D. A Method used to Compute the Sublattice Order Parameter
Appendix E. Important Constants and Relations of Atomic Physics
Index
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