99-5 P.K. Mitter, B.Scoppola

Renormalization group approach to interacting polymerised manifolds (150K, Plain TeX) Jan 7, 99

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Abstract. We propose to study the infrared behaviour of polymerised (or tethered) random manifolds of dimension $D$ interacting via an exclusion condition with a fixed impurity in $d$-dimensional Euclidean space in which the manifold is embedded. In this paper we take $D=1$, but modify the underlying free Gaussian covariance (thereby changing the canonical scaling dimension of the Gaussian random field) so as to simulate a polymerised manifold with fractional dimension $D:\ 1<D<2$. We prove rigorously, via methods of Wilson's renormalization group, the convergence to a non Gaussian fixed point for $\e>0$, sufficiently small. Here, $\epsilon=1-\beta{d\over 2}$, where $-\beta/2$ is the canonical scaling dimension of the Gaussian embedding field. Although $\epsilon$ is small, our analysis is non-perturbative in $\epsilon$. A similar model was studied earlier [CM] in the hierarchical approximation.

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