Loop statistics in the Coulomb phase

The Coulomb phase is a classical gauge field theory arising in frustrated systems with ``divergence free'' constraints, such as spin ice [1]. In this talk, we show how this phase can be understood as a loop model, and characterized by their loop length distribution and fractal dimensions [2]. Comparing similar models in 2- and 3-dimensions allows us to extract insights from connections to Stochastic-Loewner Evolution (SLE) processes, percolation and polymer physics. We mention implications of these results for related models and experiments (Heisenberg magnets, itinerant electrons [3]). \\[4pt] [1] Henley, Annual Review of Condensed Matter Physics {\bf 1}, 179 (2010).\\[0pt] [2] Jaubert, Haque, Moessner, Phys. Rev. Lett. {\bf 107}, 177202 (2011)\\[0pt] [3] Jaubert, Pitaecki, Haque \& Moessner, in preparation (2012).