### 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 1993 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

**Some rigorous results on majority rule renormalization group transformations near the critical point.** / Kennedy, Thomas G.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Some rigorous results on majority rule renormalization group transformations near the critical point

AU - Kennedy, Thomas G

PY - 1993/7

Y1 - 1993/7

N2 - 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.

AB - 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.

KW - Lattice spin system

KW - majority rule

KW - rigorous high-temperature phase

UR - http://www.scopus.com/inward/record.url?scp=21144459110&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21144459110&partnerID=8YFLogxK

U2 - 10.1007/BF01048038

DO - 10.1007/BF01048038

M3 - Article

AN - SCOPUS:21144459110

VL - 72

SP - 15

EP - 37

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 1-2

ER -