Triviality of hierarchical Ising model in four dimensions

Takashi Hara, Tetsuya Hattori, Hiroshi Watanabe

研究成果: Article査読

9 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)13-40
ページ数28
ジャーナルCommunications in Mathematical Physics
220
1
DOI
出版ステータスPublished - 2001 6 1
外部発表はい

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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