Abstract
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.
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Kennedy, T. Some rigorous results on majority rule renormalization group transformations near the critical point. J Stat Phys 72, 15–37 (1993). https://doi.org/10.1007/BF01048038
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DOI: https://doi.org/10.1007/BF01048038