Abstract
We make a few elementary observations that relate directly the items mentioned in the title. In particular, we note that when one superimposes the random current model related to the Ising model with an independent Bernoulli percolation model with well-chosen weights, one obtains exactly the FK-percolation (or random cluster model) associated with the Ising model. We also point out that this relation can be interpreted via loop-soups, combining the description of the sign of a Gaussian Free Field on a discrete graph knowing its square (and the relation of this question with the FK-Ising model) with the loop-soup interpretation of the random current model.
Highlights
We make a few elementary observations that relate directly the items mentioned in the title
We note that when one superimposes the random current model related to the Ising model with an independent Bernoulli percolation model with well-chosen weights, one obtains exactly the FK-percolation associated with the Ising model, and we point out that this relation can be interpreted via loop-soups, combining the description of the sign of a Gaussian free field on a discrete graph knowing its square with the loop-soup interpretation of the random current model
The random current model is closely related to the Ising model, and has been instrumental to prove some of its important properties
Summary
We make a few elementary observations that relate directly the items mentioned in the title. The Ising model on G with edge-weights (βe, e ∈ E) is the probability measure on Σ := {−1, +1}X defined by
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
