On monotonicity and couplings of random currents and the loop-\(\mathrm{O}(1)\)-model

Using recent couplings we provide counterexamples to monotonicity properties of percolation models related to graphical representations of the Ising model. We further prove a new coupling of the double random current model to the loop-\(\mathrm{O}(1)\)-model.

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Bibliographic Details
Published in:arXiv.org 2021-06
Main Author: Frederik Ravn Klausen
Format: Article
Language:English
Subjects:
Couplings
Graphical representations
Ising model
Percolation
Online Access:Get full text
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Summary:Using recent couplings we provide counterexamples to monotonicity properties of percolation models related to graphical representations of the Ising model. We further prove a new coupling of the double random current model to the loop-\(\mathrm{O}(1)\)-model.
ISSN:2331-8422