Continuous symmetry breaking along the Nishimori line

Christophe Garban (Université Lyon 1)

12-Oct-2021, 14:00-15:00 (2 years ago)

Abstract: I will discuss a new way to prove continuous symmetry breaking for (classical) spin systems on Z^d, d\geq 3 which does not rely on "reflection positivity". Our method applies to models whose spins take values in S^1, SU(n) or SO(n) in the presence of a certain quenched disorder called the Nishimori line. The proof of continuous symmetry breaking is based on two ingredients
1) the notion of "group synchronization" in Bayesian statistics. In particular a recent result by Abbe, Massoulié, Montanari, Sly and Srivastava (2018) which proves group synchronization when d\geq 3.
2) a gauge transformation on both the disorder and the spin configurations due to Nishimori (1981).
I will end the talk with an application of these techniques to a deconfining transition for U(1) lattice gauge theory on the Nishimori line. This is a joint work with Tom Spencer (https://arxiv.org/abs/2109.01617).

mathematical physics

Audience: researchers in the discipline

( video )


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Organizers: Margherita Disertori*, Wojciech Dybalski*, Ian Jauslin, Hal Tasaki*
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