Phase separation in a wedge. Exact results
  The exact theory of phase separation in a two-dimensional wedge is derived from the properties of the order parameter and boundary condition changing operators in field theory. For a shallow wedge we determine the passage probability for an interface with endpoints on the boundary. For generic opening angles we exhibit the fundamental origin of the filling transition condition and of the property known as wedge covariance. 
Gesualdo Delfino and Alessio Squarcini
cond-mat.stat-mech hep-th