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

29 Jun 2020 · Frederik Ravn Klausen ·

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.