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We consider near-critical two-dimensional statistical systems with boundaryconditions inducing phase separation on the strip. By exploiting low-energyproperties of two-dimensional field theories, we compute arbitrary $n$-pointcorrelation of the order parameter field. Finite-size corrections and mixedcorrelations involving the stress tensor trace are also discussed. As anexplicit illustration of the technique, we provide a closed-form expression fora three-point correlation function and illustrate the explicit form of thelong-ranged interfacial fluctuations as well as their confinement within theinterfacial region.

Multipoint correlation functions at phase separation. Exact results from field theory