Random field singularities in renormalization group transformations on Van der Waals-Ising models

Griffiths-Pearce “peculiarities” of renormalization transformations acting on nonrandom mean field Ising models are studied exactly and shown to occur in connection with critical singularities in the quenched free energies of systems with random magnetic fields. The result applies to the transformations of the full hamiltonian, considered as a function of spin configurations, and not only to the recurrence relations for its interaction constants.