Lesne A., Lagues M. Scale Invariance. From Phase Transitions to Turbulence

Springer,2008,414 p. The opalescence of a fluid near its critical point has been a matter of curiosity for more than 100 years. However, the organisation of a fluid as it wavers between a liquid and a vapour was only understood 40 years ago – thanks to a profound insight by Leo Kadanoff in what was a major cultural achievement. We also know of other self-similar systems: fractals (structures resulting from quite simple geometrical constructions) and turbulent flows (which we still struggle to control). But the case of critical points has become the key example: difficult but accessible to reasoning and all embracing enough to manifest widely varying families of behaviours.
The techniques of calculation (the renormalisation group) are given in many works and brought together in the fine book by Toulouse and Pfeuty. But a book giving the panorama was needed: this is it. It starts with liquids and gases but it also shows the multiple scales that we meet in Brownian motion, flexible polymers or percolation clusters. Furthermore, the book is bold enough to address questions that are still open: cuprate superconductors, turbulence, etc. The most controversial question, which appears in the final chapter, is that of self-organised criticality.
For some this is a whole new world, and for others a world of mere words. But in any case, this book gives an accessible picture of example cases in which uncertainties still remain. And more generally it invites the reader to think. A good plan for young people curious about science.Pierre-Gilles de Gennes