# Remaining models conjectured to converge to SLE(6) or CLE(6)

I am wondering which models are conjectured (eg. numerically) to converge to SLE(6) (Schramm-Loewner evolution with $$\kappa=6$$) or CLE(6) (conformal loop ensemble). I am searching for a research topic in this very interesting area.

The following are from Smirnov's 2007 review and elsewhere:

1) Critical percolation for lattices other than triangular eg. the square lattice. Any detailed review on this?

2) Fortuin-Kasteleyn random cluster model for $$n=1$$ and $$x>x_{c}$$, where $$x_{c}$$ the critical edge weight.

3) For $$O(1)$$ but for $$x\neq 1$$ and $$p\neq 1/2$$, which correspond to the critical percolation case.

4) In the article "conformal invariance of hydrodynamic turbulence", they showed numerically that zero-vorticity isolines correspond to SLE(6).

5) Random-field Ising model by Stevenson (2011).