On monotonicity and couplings of random currents and the loop-$\mathrm{O}(1)$-model
Mathematical Physics
2022-11-02 v2 math.MP
Probability
Abstract
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--model.
Cite
@article{arxiv.2006.15897,
title = {On monotonicity and couplings of random currents and the loop-$\mathrm{O}(1)$-model},
author = {Frederik Ravn Klausen},
journal= {arXiv preprint arXiv:2006.15897},
year = {2022}
}
Comments
7 pages, 4 figures, 4 tables