Renormalization Group Theory

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.