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))
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.