This lecture introduces the variational method in the Random Field Ising Model (RFIM), explaining the cost function and the competition between minimizing the cost and aligning with a random field. The instructor discusses the algorithmic questions, the Gibbs inequality, and the Gibbs free energy. The lecture explores the variational method, the Gauchan-Poincaré inequality, and the Cality method for computing the free energy. It concludes with a discussion on the convergence of the free entropy and the importance of techniques like Cality and replica in statistical physics.