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Abstract
摘要
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The mixed p-spin models (defined on discrete hypercubes or on spheres) are typical mean field spin glass models, which were introduced as approximation of the more realistic short range models in the 1970s. The celebrated Sherrington-Kirkpatrick (SK) model is a special mixed p-spin model. Starting in 1979, Giorgio Parisi wrote a series of ground breaking papers introducing the idea of replica symmetry breaking (RSB), which allowed him to predict a solution for the SK model by breaking the symmetry of replicas infinitely many times at low temperature. In this talk, we will show that in a certain sense Parisi's prediction holds at zero temperature for the Ising mixed p-spin model. On the other hand, we will show that there exist two-step RSB spherical mixed p-spin glass models at zero temperature. This talk is based on joint works with Antonio Auffinger (Northwestern University) and Wei-Kuo Chen (University of Minnesota).
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