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

Frederik Ravn Klausen

paper

On monotonicity and couplings of random currents and the loop- $O (1)$ -model

arXiv:2006.15897

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- $O (1)$ -model.

7 pages, 4 figures, 4 tables

References in corpus (1)

Marginal triviality of the scaling limits of critical 4D Ising and $ϕ_{4}^{4}$ models

On monotonicity and couplings of random currents and the loop-O(1)-model

Abstract

References in corpus (1)

On monotonicity and couplings of random currents and the loop- $O (1)$ -model