## 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.

Original language | English (US) |
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Pages (from-to) | 15-37 |

Number of pages | 23 |

Journal | Journal of Statistical Physics |

Volume | 72 |

Issue number | 1-2 |

DOIs | |

State | Published - Jul 1 1993 |

## Keywords

- Lattice spin system
- majority rule
- rigorous high-temperature phase

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics