Presenting and developing the theory of spin glasses as a prototype for complex systems, this book is a rigorous and up-to-date introduction to their properties. The book combines a mathematical description with a physical insight of spin glass models. Topics covered include the physical origins of those models and their treatment with replica theory; mathematical properties like correlation inequalities and their use in the thermodynamic limit theory; main exact solutions of the mean field models and their probabilistic structures; and the theory of the structural properties of the spin glass phase such as stochastic stability and the overlap identities. Finally, a detailed account is given of the recent numerical simulation results and properties, including overlap equivalence, ultrametricity and decay of correlations. The book is ideal for mathematical physicists and probabilists working in disordered systems.

'This is a dense and concise review about a large spectrum of topics, related to equilibrium statistical mechanics of disordered systems, in particular spin glasses, on which the Authors have given recent relevant contribution … rigorous, but quite simple, with complete details filled in great clarity.' Journal of Statistical Physics

Pierluigi Contucci is Professor of Mathematical Physics at the University of Bologna and Research Director for the hard sciences section of the Istituto Cattaneo. His research interests are in statistical mechanics and its applications to socio-economic sciences. Cristian Giardinà is Associate Professor in Mathematical Physics at the University of Modena and Reggio Emilia and Visiting Professor in Probability at Nijmegen University. His research interests are in mathematical statistical physics and stochastic processes.