Lupu, Titus; Werner, Wendelin A note on Ising random currents, Ising-FK, loop-soups and the Gaussian free field. (English) Zbl 1338.60236 Electron. Commun. Probab. 21, Paper No. 13, 7 p. (2016). Summary: 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, 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 (and the relation of this question with the FK-Ising model) with the loop-soup interpretation of the random current model. Cited in 14 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics Keywords:Ising model; random currents; loop-soups; Gaussian free field PDF BibTeX XML Cite \textit{T. Lupu} and \textit{W. Werner}, Electron. Commun. Probab. 21, Paper No. 13, 7 p. (2016; Zbl 1338.60236) Full Text: DOI Euclid arXiv