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Résumé |
The structure of the Sachdev-Ye-Kitaev (SYK) model is strikingly similar to the canonical mean-field models
of spin glass theory, yet the resulting behavior is quite different --- the SYK model is "maximally chaotic" and
has connections to quantum gravity at low temperature, whereas spin glasses instead have frozen dynamics
and an intricate equilibrium structure. In the first part of this talk, we present some explanation as to why, by
proving the following result: in any bosonic model with all-to-all random interactions, there must be a
breakdown of self-averaging of the partition function, and thus the analysis used to study the (fermionic) SYK
model cannot directly apply. In this sense, the fermionic nature of the SYK model is a necessary ingredient for
its physics. In the second part of the talk, we consider the physical implications of a breakdown of self-
averaging in more detail. We show that, surprisingly, self-averaging transitions need *not* be related to any
spin glass physics. Doing so requires resolving some ambiguities in the replica trick that appear to have gone
unaddressed until now.
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