Abstract
The talk reviews Parisi's mean field theory for an Ising spin glass, with emphasis on its stability properties and physical interpretation. Next, as a first step towards physical, shortrange systems, quadratic fluctuations around this mean field solution are considered and shown to be finite, despite the presence of an infinity of soft modes in the theory. Working out the first corrections to the equation of state beyond the Gaussian approximation, however, it is found that divergences begin to plague the theory in any dimension, once interactions between fluctuations are taken into account. A preliminary analysis of higher orders indicates how the perturbation series is to be rearranged to obtain a meaningful theory.
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