Triviality of hierarchical Ising model in four dimensions

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 xed point. Convergence of the subsequent trajectory to the Gaussian xed point is shown by power decay of the eeective 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 xed point, characteristic functions and Newman's inequalities are systematically used.