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

Non-periodic long-range order for fast decaying interactions at positive temperatures

We present the first example of an exponentially decaying interaction which gives rise to non-periodic long-range order at positive temperatures.Comment: 7 pages, Late