A conformal loop ensemble is a family of probability laws on collections of planar loops that is invariant under
conformal mappings and satisfies a spatial restriction
property. After the loops meeting a specified region are
revealed, the remaining loops in each unrevealed connected
component have the corresponding conformal loop ensemble law. The simple-loop
ensembles form a one-parameter family 
, 
(Sheffield and Werner 2012).
Averous et al. (2026) reported that the loops of the critical planar random-cluster model
with 
on the square integer lattice 
converge in the scaling limit to 
. The associated four-state Potts
model therefore has a conformally invariant scaling limit.
