### Synopses & Reviews

In 1982 the founder of renormalization group (RG) theory, Kenneth G. Wilson, was awarded by the Nobel price in physics for his pioneering contribution to the development of solid state theory. RG theory constitutes perhaps the most important progress in theoretical physics since the development of quantum mechanics. Up to now the achievements of RG theory were nearly not recognized by experimental physicists. In the present generation of textbooks on physics this theory is not dealt with. This book aims to overcome this deficiency in a twofold way. First, the fundamentals and principles of RG theory will be demonstrated on account of practical experimental examples and, second, the reader will become able to analyze and interpret his own experimental data on the advanced level of RG theory. At the same time it will become apparent how the shortcomings and analytical failures of conventional theories such as the spin wave theory of magnetism or the BCS theory of superconductivity are revealed by RG theory. These two theories give no correct account of the continuous dynamic symmetry in the ordered state and appear as preliminary steps only towards a complete understanding of collective ordering phenomena in solids. In particular classification of all ordered materials according to a small number of universality classes is beyond the scope of classical theories. A final theory of the long range ordered state is, however, not in view. This ambitious task will still request enormous experimental and theoretical efforts. RG theory is more a methodical tool towards this goal rather than a final solution of this problem. This book, therefore, restricts on a systematic and phenomenological overview over those experimental facts that are completely consistent with RG theory but in disagreement with conventional theories. In other words, it provides the basis for the development of the next generation of solid state theories.

The book will be an indispensable reference for solid state experimentalists. It demonstrates the principles of RG theory on account of many experimental examples. The most important consequence for the experimentalist is that all ordered materials can be classified according to a small number of universality classes. This provides a reliable basis for the characterisation of all materials in the long range ordered state. Since the book comprises a large number of phenomena and experimental analyses that are in disagreement with conventional theories it will be most interesting also for theorists as a starting point for the development of advanced theoretical concepts for the long range ordered state.

#### Synopsis

Spin wave theory of magnetism and BCS theory of superconductivity are typical theories of the time before renormalization group (RG) theory. The two theories consider atomistic interactions only and ignore the energy degrees of freedom of the continuous (infinite) solid. Since the pioneering work of Kenneth G. Wilson (Nobel Prize of physics in 1982) we know that the continuous solid is characterized by a particular symmetry: invariance with respect to transformations of the length scale. Associated with this symmetry are particular field particles with characteristic excitation spectra. In diamagnetic solids these are the well known Debye bosons. This book reviews experimental work on solid state physics of the last five decades and shows in a phenomenological way that the dynamics of ordered magnets and conventional superconductors is controlled by the field particles of the infinite solid and not by magnons and Cooper pairs, respectively. In the case of ordered magnets the relevant field particles are called GSW bosons after Goldstone, Salam and Weinberg and in the case of superconductors the relevant field particles are called SC bosons. One can imagine these bosons as magnetic density waves or charge density waves, respectively. Crossover from atomistic exchange interactions to the excitations of the infinite solid occurs because the GSW bosons have generally lower excitation energies than the atomistic magnons. According to the principle of relevance the dynamics is governed by the excitations with the lowest energy. The non relevant atomistic interactions with higher energy are practically unimportant for the dynamics.

#### Synopsis

This book reviews experimental work on solid state physics and shows in a phenomenological way that the dynamics of ordered magnets and conventional superconductors is controlled by field particles of the infinite solid and not by magnons and Cooper pairs.

### Table of Contents

1. Introduction.- 2. History of conventional spin wave theory.- 3. Basic issues of Renormalization Group (RG) theory.- 4. Universality.- 5. Microscopic processes.- 6. Non-relevant magnons.- 7. Crossover phenomena.- 8. Metastability of universality classes.- 9. Relevant and non relevant interactions.- 10. Temperature dependence of the magnon excitation spectra.- 11. Magnetic heat capacity.- 12. Experimental verification of GSW bosons.- 13. Magnets with and without magnon gap (Goldstone mode).- 14. Microscopic details: spin structure, site disorder, two order parameters.- 15. The critical magnetic behaviour.- 16. Thermal lattice expansion and magnetostriction.- 17. The total energy content.- 18. Superconductivity.- 19. Conclusions.