Certain approximate renormalization-group recursion relations are exact for Ising models on special hierarchical lattices, as noted by Berker and Ostlund. These lattice models provide numerous examples of phase coexistence and critical points at finite temperatures, including cases of continuously varying critical exponents and phase transitions without phase coexistence. The lattices are, typically, quite inhomogeneous and may possess several inequivalent limits as infinite lattices.

• Received 1 April 1981

DOI:https://doi.org/10.1103/PhysRevB.24.496