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The study of spin glasses is a fascinating new topic in condensed matter physics that has attracted considerable attention over recent years. This book gives a comprehensive account of the subject, and will provide a valuable overview and reference to both newcomers and experts in the field. The authors discuss the most important developments in the theory, experimental work and computer modelling of spin glasses. The first chapters give a general introduction to the basic concepts, followed by a discussion of mean field theory, the only well-established spin glass theory so far. This book will be of interest primarily to condensed matter physicists, but because of the potentially wide applications of the theory involved, the book should also appeal to researchers in other disciplines, including theoretical physics, metallurgy and computational neuroscience.

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We study pairwise Ising models for describing the statistics of multi-neuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their statistical properties. To do this, we extract the optimal couplings for subsets of size up to 200 neurons, essentially exactly, using Boltzmann learning. We then study the quality of several approximate methods for finding the couplings by comparing their results with those found from Boltzmann learning. Two of these methods -inversion of the TAP equations and an approximation proposed by Sessak and Monasson -are remarkably accurate. Using these approximations for larger subsets of neurons, we find that extracting couplings using data from a subset smaller than the full network tends systematically to overestimate their magnitude. This effect is described qualitatively by infinite-range spin glass theory for the normal phase. We also show that a globally-correlated input to the neurons in the network lead to a small increase in the average coupling. However, the pair-to-pair variation of the couplings is much larger than this and reflects intrinsic properties of the network. Finally, we study the quality of these models by comparing their entropies with that of the data. We find that they perform well for small subsets of the neurons in the network, but the fit quality starts to deteriorate as the subset size grows, signalling the need to include higher order correlations to describe the statistics of large networks.