6 papers
The End of the Double Random Current
Ulrik Thinggaard Hansen, Frederik Ravn Klausen
The Ising correlation function can be expressed in terms of connectivity probabilities of a random graph known as the double random current. In 2016, Duminil-Copin asked whether th…
The Supercritical Loop O(1) and Random Current models: Uniqueness and Mixing
Ulrik Thinggaard Hansen, Frederik Ravn Klausen
Much recent rigorous study of the classical ferromagnetic Ising model has been powered by its graphical representations, such as the random current and loop O(1) model (high temper…
A General Coupling for Ising Models and Beyond
Ulrik Thinggaard Hansen, Jianping Jiang, Frederik Ravn Klausen
The couplings between the Ising model and its graphical representations, the random-cluster, random current and loop models, are put on common footing through a gen…
Non-uniqueness of phase transitions for graphical representations of the Ising model on tree-like graphs
Ulrik Thinggaard Hansen, Frederik Ravn Klausen, Peter Wildemann
We consider the graphical representations of the Ising model on tree-like graphs. We construct a class of graphs on which the loop model and the single random curre…
The Uniform Even Subgraph and Its Connection to Phase Transitions of Graphical Representations of the Ising Model
Ulrik Thinggaard Hansen, Boris Kjær, Frederik Ravn Klausen
The uniform even subgraph is intimately related to the Ising model, the random-cluster model, the random current model, and the loop (1) model. In this paper, we first…
Strict monotonicity, continuity and bounds on the Kertész line for the random-cluster model on
Ulrik Thinggaard Hansen, Frederik Ravn Klausen
Ising and Potts models can be studied using the Fortuin-Kasteleyn representation through the Edwards-Sokal coupling. This adapts to the setting where the models are exposed to an e…