Electronic Communications in Probability

A note on Ising random currents, Ising-FK, loop-soups and the Gaussian free field

Titus Lupu and Wendelin Werner

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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, 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.

Article information

Source
Electron. Commun. Probab., Volume 21 (2016), paper no. 13, 7 pp.

Dates
Received: 27 November 2015
Accepted: 12 January 2016
First available in Project Euclid: 17 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1455717135

Digital Object Identifier
doi:10.1214/16-ECP4733

Mathematical Reviews number (MathSciNet)
MR3485382

Zentralblatt MATH identifier
1338.60236

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

Keywords
Ising model random currents loop-soups Gaussian free field

Rights
Creative Commons Attribution 4.0 International License.

Citation

Lupu, Titus; Werner, Wendelin. A note on Ising random currents, Ising-FK, loop-soups and the Gaussian free field. Electron. Commun. Probab. 21 (2016), paper no. 13, 7 pp. doi:10.1214/16-ECP4733. https://projecteuclid.org/euclid.ecp/1455717135


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