Problems with the definition of renormalized Hamiltonians for   momentum-space renormalization transformations
  For classical lattice systems with finite (Ising) spins, we show that the implementation of momentum-space renormalization at the level of Hamiltonians runs into the same type of difficulties as found for real-space transformations: Renormalized Hamiltonians are ill-defined in certain regions of the phase diagram. 
Aernout C. D. van Enter and Roberto Fern\'andez