Triviality of hierarchical Ising model in four dimensions

Takashi Hara, Tetsuya Hattori, Hiroshi Watanabe

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2001 Jun 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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