The material here is self-contained and should be accessible to students with a basic knowledge of theoretical physics and statistical mechanics. It has been used for a one-term graduate lecture course at the Landau Institute for Theoretical Physics.
Contents:The Ising Magnetic SystemsPhysics of the Spin Glass StateReplica MethodReplica Symmetry BreakingPhysics of Replica Symmetry BreakingReplica Symmetry Breaking Solution Near TcUltrametricityScaling in the Space of Spin Glass StatesExperimentsPartial AnnealingStatistical Models of Neural NetworksThe Hopfield ModelPartial Annealing in Neural NetworksOther Kinds of Neural NetworksAppendix: Stability of the Replica-Symmetric Solutions
Readership: Researchers and graduate students in statistical mechanics and neural networks.
“The book by Viktor Dotsenko in large parts presents the most important results of this research based on the replica method. Although these results have been presented systematically already elsewhere (for instance in the well-known book by Amit) their concise presentation makes the book self-contained and a good introduction to the theoretical tools.”Mathematics Abstracts