Aukosh Jagannath (Waterloo)
Probability Seminar
Title:听Replica Symmetry Breaking, Shattering, and Metastability
础产蝉迟谤补肠迟:听The statics and dynamics of mean-field models of spin glasses have been studied in-depth by the physics community since the '70s. At the heart of this is the trade-off between the notions of replica symmetry breaking, shattering, and metastability. I will survey the current mathematical understanding of these ideas in the 鈥渟imple鈥� case of the spherical听p-spin model. I will start by recalling how the landscape complexity听can be used to听understand of the 鈥渞eplica symmetry breaking鈥� phase following听the work of Auffinger鈥揃en Arous鈥揅erny and Subag. I'll then turn to our recent joint work with Ben Arous on the 鈥渞eplica symmetric鈥� phase. Here we prove the existence of a shattering phase and show that metastable states exist up to an even higher temperature as predicted by Barrat鈥揃urioni鈥揗ezard. This latter work is based on a Thouless鈥揂nderson鈥揚almer decomposition which builds on the ideas of Subag. I will end by presenting a series of open questions and conjectures surrounding sharp phase boundaries for shattering and metastability.听
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Online seminar via zoom, for more information please write to Seminar [at] problab.ca
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