Hosaka K.
Triviality of Hierarchical Models with Small Negative
$\phi^4$ Model in Four Dimensions
(341K, Postscript)
ABSTRACT. We investigate trajectories of the Kadanoff-Wilson renormalization group (RG) acting on a Gaw\c{e}dzki-Kupiainen's hierarchical spin model in 4 dimensions with the following initial single spin potential;
$v_{0}(\phi_{x})= \mu_{0} \phi_{x}^{2}-\lambda_{0} \phi_{x}^{4}
+\rho_{0} \phi_{x}^{6}$ in a weak coupling regime. We prove that
under a suitable conditions on $\mu_{0}$, $\lambda_{0}$, $\rho_{0}$ there exists a trajectory which leads to a Gaussian fixed point using Gaw\c{e}dzki and Kupiainen's method.