Variational Method in RFIM

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.