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Phase transition in lattice permutations and uniformly positive correlations in the dimer model in Zd, d > 2, via reflection positivity

Oberseminar Darmstadt

Datum: 05.12.2019

Zeit: 16:15–17:45 Uhr

ABSTRACT: Our first main result is that correlations between monomers in the dimer model on Zd do not decay to zero when d > 2. This is the first rigorous result about correlations in the dimer model in dimensions greater than two and shows that the model behaves drastically differently than in two dimensions, in which case it is integrable and correlations are known to decay to zero algebraically. Such a result is implied by our more general, second main result, which states the occurrence of a phase transition in the model of lattice permutations, which is related to the quantum Bose gas. More precisely, we consider a self-avoiding walk interacting with lattice permutations and we prove that, in the regime of fully-packed loops, such a walk is ‘long’ and the distance between its end-points grows linearly with the diameter of the box. These results follow from the derivation of an Infrared-ultraviolet bound from a new general probabilistic settings, with coloured loops and walks interacting at sites and walks entering into the sys- tem from some ‘virtual’ vertices. 


Lorenzo Taggi, WIAS Berlin


TU Darmstadt S2|15 Raum 401
Schlossgartenstr. 7, 64289 Darmstadt


Technische Universität Darmstadt

Fachbereich Mathematik - Stochastik
Schlossgartenstraße 7
64289 Darmstadt
Telefon: +49 6151 16-23380
Telefax: +49 6151 16-23381


Goethe-Universität Frankfurt am Main, Johannes Gutenberg-Universität Mainz

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