Since their discovery, spin glasses have proved to be a fascinating field of research in modern Solid State Physics for which a number of mathematical models have been proposed. The origin of this notoriety relies on the combination of randomly distributed spines inducing a series of remarkable properties of the underlying substance which goes from different magnetization behaviours to abnormal phase transitions. The book under review gives a gentle introduction of the basic definitions, main models and current applications of them, aimed at a wide audience of scientists, social scientist and anyone interested in complexity science. This is neither a book of Mathematics, nor an in-depth study in Physics, and the reader is only required to have introductory college-level notions in Mathematics and Physics.

The authors are well-known researchers in complex systems with contributions (both monographs and articles) on the topic of the book. In particular, the book was initially motivated by the lectures given by one of them in a summer course on complexity. The book offers the reader a combination of three main ingredients. Firstly, together with an initial introduction to order, symmetry and organization of matter, the main experiments which originated the notion of spin glasses are presented. Then the main mathematical models to describe these glasses are introduced to finally show the applications of these mathematical constructions in a varied range of situations and branches of Science. In my opinion, this applied part is the most stimulating for it shows the connections between apparently different subjects. In general, the work is well presented and the reader will surely find it both inspiring and interesting.

Reviewer:

Marco Castrillon Lopez