Some rigorous results on majority rule renormalization group transformations near the critical point

• DOI: 10.1007/bf01048038
• Publication Date: 2005-01-26T05:56:22Z
• Authors: Tom Kennedy
• Keywords: Lattice (music); Critical point (mathematics); Square lattice

We consider the majority rule renormalization group transformation with two-by-two blocks for the Ising model on a two-dimensional square lattice. For three particular choices of the block spin configuration we prove that the model conditioned on the block spin configuration remains in the high-temperature phase even when the temperature is slightly below the critical temperature of the ordinary Ising model with no conditioning. We take as the definition of the infinite-volume limit an equation introduced in earlier work by the author. We use a computer to find an approximate solution of this equation and verify a condition which implies the existence of an exact solution.