04-256 Hosaka K.

Triviality of Hierarchical Models with Small Negative $\phi^4$ Model in Four Dimensions (341K, Postscript) Aug 19, 04

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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.

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