Abstract
The sixth lecture presented several aspects of the theory of polymers in random media. They are one of the most studied systems in disordered systems theory. The lecture began by showing the difference between annealed and frozen averages. Then it was shown that polymers in random media exhibit a phase transition in dimension greater than three, with a high-temperature phase where the polymer is delocalized and a low-temperature phase where the polymer is trapped. In dimensions less than or equal to three, only the trapped phase remains. The lecture went on to show how the solution of the Lieb Liniger model by Bethe's ansatz enables us to calculate the free energy of directed polymers in dimension 1 + 1 using the replica method.
