00-397 Takashi Hara, Tetsuya Hattori, Hiroshi Watanabe

Triviality of hierarchical Ising model in four dimensions (107K, AMS-LaTeX with an EPS figure, and C codes (compressed)) Oct 6, 00

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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. (For mp_arc) We also include source codes of computer programs (written in C++), which were used to prove the main result of this paper.

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