In this talk, I will explain the path integral formulation of the two-dimensional massless Sinh–Gordon model from the probabilistic perspective, and discuss the study of the free energy in the infinite volume limit. More specifically, I will explain how the asymptotic order can be established by suitable reductions to the analysis of small deviations of Gaussian multiplicative chaos, and highlight various ingredients in our proof. This is based on joint work with Nikolay Barashkov and Joona Oikarinen.