Long range correlations generated by phase separation. Exact results   from field theory
  We consider near-critical planar systems with boundary conditions inducing phase separation. While order parameter correlations decay exponentially in pure phases, we show by direct field theoretical derivation how phase separation generates long range correlations in the direction parallel to the interface, and determine their exact analytic form. The latter leads to specific contributions to the structure factor of the interface. 
Gesualdo Delfino and Alessio Squarcini
cond-mat.stat-mech hep-th