What discrete processes/models have been proven to have scaling limits to $\text{SLE}(\kappa)$, for various $\kappa$?
I know about loop-erased random walk and uniform spanning trees.
What about conjectures in this direction? (Such as the double-dimer-cover cycles, which I read are conjectured to be $\text{SLE}(4)$)


I'm very new to this, so if you please could, together with the answer refer to a paper/article/survey accompanying the result, that would be greatly appreciated!



Models with SLE scaling limit
There are several other models proved to converge to SLE: critical percolation on the triangular lattice, Gaussian Free Field, Harmonic Explorer, and recently also the critical Ising model. You can check the paper Kevin linked or [Schramm's slides](http://dbwilson.com/schramm/memorial/ICM.pdf) from ICM2006 for some highlights. Just keep in mind that this is a fast changing field at the moment so there has been some progress since 2006.


