Gibbs thermodynamic potentials for disordered systems

We propose a new method to estimate the quenched free energy in disordered systems. It uses generalized thermodynamic potentials, given by annealed averages of the partition function with appropriate constraints realized by the aid of Lagrange multipliers. The method is applied to Ising models with random magnetic fields. In that particular case, the constraints correspond to averaging only over the disorder configurations where the sum of the random variables has the correct mean value and variance.