  Using an alternative notion of entropy introduced by Datta, the max-entropy,
we present a new simplified framework to study the minimizers of the specific
free energy for random fields which are weakly dependent in the sense of Lewis,
Pfister, and Sullivan. The framework is then applied to derive the variational
principle for the loop $O(n)$ model and the Ising model in a random percolation
environment in the nonmagnetic phase, and we explain how to extend the
variational principle to similar models. To demonstrate the generality of the
framework, we indicate how to naturally fit into it the variational principle
for models with an absolutely summable interaction potential, and for the
random-cluster model.
