Probability measures and Hamiltonian models on Bethe lattices. II. The solution of thermal and configurational problems

In a previous paper we introduced a method for the construction of rotationally and translationally invariant probability measures generated by one‐step Markov Hamiltonian models on q‐state‐site Bethe lattices. Here, the corresponding thermal problems are solved by finding the relative free energy, which gives complete information on the properties of the models under study. Configurational problems also can be solved with the present tools. As an example, the solution of polychromatic correlated‐site/random‐bond percolation models is found.