 04256 Hosaka K.
 Triviality of Hierarchical Models with Small Negative
$\phi^4$ Model in Four Dimensions
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Aug 19, 04

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Abstract. We investigate trajectories of the KadanoffWilson renormalization group (RG) acting on a Gaw\c{e}dzkiKupiainen'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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