|Date:||Tue, September 21, 2021|
|Place:||Room 120 Research I and online via zoom (please write the organizer (s.petrat AT jacobs-university.de) for the meeting id and passcode)|
Abstract: Subject of our considerations is a spectral theoretic application of the Witten Laplacian in classical statistical mechanical lattice spin systems in the limit of high temperatures. The involved Hamiltonian function consists of an on-site potential term given by even polynomials and a finite range interaction term, both of which are not assumed to be translation invariant. In particular, no specific spatial structure is imposed on the model.
For such systems, we establish existence and uniqueness of the associated Gibbs measure in the thermodynamic limit. Using this, we show exponential decay of the correlations and, what is more, we derive the correlation asymptotics in terms of a metric inherent to the model that is primarily governed by the underlying interaction rather than the geometry of the lattice. The spectral gap of the Witten Laplacian plays a crucial and recurring role throughout the proofs. This is joint work with V. Bach.