Triviality of hierarchical Ising model in four dimensions

Takashi Hara, Tetsuya Hattori, Hiroshi Watanabe

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 languageEnglish
Pages (from-to)13-40
Number of pages28
JournalCommunications in Mathematical Physics
Volume220
Issue number1
DOIs
Publication statusPublished - 2001 Jun
Externally publishedYes

Fingerprint

Hierarchical Model
Ising model
Ising Model
Fixed point
Renormalization Group
trajectories
Trajectory
Critical Group
characteristic equations
Strong Coupling
Characteristic Function
iteration
Decay
Iteration
decay

ASJC Scopus subject areas

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

Cite this

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

In: Communications in Mathematical Physics, Vol. 220, No. 1, 06.2001, p. 13-40.

Research output: Contribution to journalArticle

Hara, Takashi ; Hattori, Tetsuya ; Watanabe, Hiroshi. / Triviality of hierarchical Ising model in four dimensions. In: Communications in Mathematical Physics. 2001 ; Vol. 220, No. 1. pp. 13-40.
@article{a7687c02474645e4a36c125e2e1f1653,
title = "Triviality of hierarchical Ising model in four dimensions",
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.",
author = "Takashi Hara and Tetsuya Hattori and Hiroshi Watanabe",
year = "2001",
month = "6",
doi = "10.1007/s002200100440",
language = "English",
volume = "220",
pages = "13--40",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "1",

}

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 -