Written for researchers in the field with different professional backgrounds, this volume classifies phenomena not by system but rather by the type of competing interactions involved. This allows for a straightforward presentation of the underlying principles and the universal laws governing the behaviour of different systems.
Starting with a historical overview, the author proceeds by describing self–competitions of various types of interactions (such as diploar or multipolar interactions), competitions between a short–range and a long–range interaction (as in Ising systems or DNA models) or between a long–range interaction and an anisotropy (as in ultrathin magnetic films or magnetic nanoparticles) and finally competitions between interactions of the same range (as in spin glasses).
Each chapter contains a few problems with solutions which provide suitable material for lecturers of mathematics and physics as well as biology courses.
A vast body of references to the original literature make the volume self–contained and ideally suited to master this interdisciplinary field.
1.1 How the story begun
1.2 First theoretical approaches for competing interactions
1.3 Beautiful patterns govern the world
2. Self–competition or how to choose the best from the worse
2.1 Frustration: the world is not perfect
2.2 Self–competition of the short–range interactions
2.3 Self–competition of the long–range interactions
2.4 Ordering entropy
3. Famous competition between a short– and a long–range interaction
3.1 Localized particles
3.2 Delocalized particles
4. Competition between a long–range dipolar interaction and an anisotropy
4.1 Ultrathin magnetic films
4.2 Ultrthin magnetic particles
5. Competition between two interactions of the same range
5.1 Two short–range interactions
5.2 Two long–range interactions
6. Dynamics of self–organized systems close to equilibrium
6.1 Polarization reversal
6.2 Wave phenomena
6.3 Diffusion–limited aggregation
6.4 Dynamics of nanoparticles