Preface

Summary

Geometrical Frustration! Such a title requires at least two preliminary remarks. First, this book is about condensed matter physics, and in particular cases where matter is spatially organized in complex structures like large cell crystals, glasses, quasicrystals, and also some liquid crystal organizations. The second remark concerns using the word ‘frustration’. Let us immediately rule out its psychological meaning, and keep only its technical one, introduced about 20 years ago in the context of spin glasses, and which subsequently diffused to neighbouring fields, thanks to physical analogies. Indeed, we hope to demonstrate that, studying ‘frustrated systems’, far from generating any frus- tration, will create satisfaction linked to a better understanding of a rich and complex domain.

Geometrical frustration covers situations where a certain type of local order, favoured by physical interactions, cannot propagate throughout space. A classical example is that of pentagonal, or icosahedral, order which appears in the three-dimensional sphere packing problem. This symmetry, which is not compatible with translations, is nevertheless met, often imperfectly, in numerous materials. Such strong contradictions between local and global configurations are found in various physical systems, with different kinds of interactions, and coherence sizes. The concept of frustration then applies to metallic alloys at the atomic scale, to liquid crystal organizations like amphiphiles films or cholesteric blue phases at the scale of hundreds of thousands of ångströms, and even to larger scales with some biological structures.