### Abstract

Existence of critical renormalization group trajectory for a hierarchical Ising model in 4 dimensions is shown. After 70 iterations of renormalization group transformations, the critical Ising model is mapped into a vicinity of the Gaussian fixed point. Convergence of the subsequent trajectory to the Gaussian fixed point is shown by power decay of the effective coupling constant. The analysis in the strong coupling regime is computer-aided and Newman's inequalities on truncated correlations are used to give mathematical rigor to the numerical bounds. In order to obtain a criterion for convergence to the Gaussian fixed point, characteristic functions and Newman's inequalities are systematically used.

Original language | English |
---|---|

Pages (from-to) | 13-40 |

Number of pages | 28 |

Journal | Communications in Mathematical Physics |

Volume | 220 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2001 Jun |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*220*(1), 13-40. https://doi.org/10.1007/s002200100440

**Triviality of hierarchical Ising model in four dimensions.** / Hara, Takashi; Hattori, Tetsuya; Watanabe, Hiroshi.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 220, no. 1, pp. 13-40. https://doi.org/10.1007/s002200100440

}

TY - JOUR

T1 - Triviality of hierarchical Ising model in four dimensions

AU - Hara, Takashi

AU - Hattori, Tetsuya

AU - Watanabe, Hiroshi

PY - 2001/6

Y1 - 2001/6

N2 - Existence of critical renormalization group trajectory for a hierarchical Ising model in 4 dimensions is shown. After 70 iterations of renormalization group transformations, the critical Ising model is mapped into a vicinity of the Gaussian fixed point. Convergence of the subsequent trajectory to the Gaussian fixed point is shown by power decay of the effective coupling constant. The analysis in the strong coupling regime is computer-aided and Newman's inequalities on truncated correlations are used to give mathematical rigor to the numerical bounds. In order to obtain a criterion for convergence to the Gaussian fixed point, characteristic functions and Newman's inequalities are systematically used.

AB - Existence of critical renormalization group trajectory for a hierarchical Ising model in 4 dimensions is shown. After 70 iterations of renormalization group transformations, the critical Ising model is mapped into a vicinity of the Gaussian fixed point. Convergence of the subsequent trajectory to the Gaussian fixed point is shown by power decay of the effective coupling constant. The analysis in the strong coupling regime is computer-aided and Newman's inequalities on truncated correlations are used to give mathematical rigor to the numerical bounds. In order to obtain a criterion for convergence to the Gaussian fixed point, characteristic functions and Newman's inequalities are systematically used.

UR - http://www.scopus.com/inward/record.url?scp=0035534916&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035534916&partnerID=8YFLogxK

U2 - 10.1007/s002200100440

DO - 10.1007/s002200100440

M3 - Article

AN - SCOPUS:0035534916

VL - 220

SP - 13

EP - 40

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -