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

zbMath1482.82015arXiv2006.15897MaRDI QIDQ5026472

Frederik Ravn Klausen

Publication date: 8 February 2022

Full work available at URL: https://arxiv.org/abs/2006.15897

zbMATH Keywords

Ising modelrandom currentsEulerian percolationpercolation with degree constraints

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Phase transitions (general) in equilibrium statistical mechanics (82B26) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (1)

Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Zd

Cites Work

• A note on Ising random currents, Ising-FK, loop-soups and the Gaussian free field
• Geometric analysis of \(\phi^ 4\) fields and Ising models. I, II
• Random even graphs
• Random currents expansion of the Ising model
• Marginal triviality of the scaling limits of critical 4D Ising and \(\phi_4^4\) models
• The planar Ising model and total positivity
• Emergent planarity in two-dimensional Ising models with finite-range interactions
• Lectures on the Ising and Potts Models on the Hypercubic Lattice
• Does Eulerian percolation on $Z^2$ percolate ?
• The Random-Cluster Model
• Statistics of the Two-Dimensional Ferromagnet. Part I

This page was built for publication: On monotonicity and couplings of random currents and the loop-$\mathrm{O}(1)$-model