We consider continuous and discrete (1+1)-dimensional wetting models which undergo a localization/delocalization phase transition. Using a simple approach based on Renewal Theory we determine the precise asymptotic behavior of the partition function, from which we obtain the scaling limits of the models and an explicit construction of the infinite volume measure in all regimes, including the critical one.
"Sharp asymptotic behavior for wetting models in (1+1)-dimension." Electron. J. Probab. 11 345 - 362, 2006. https://doi.org/10.1214/EJP.v11-320