P.K. Mitter, B.Scoppola
Renormalization group approach to 
interacting polymerised manifolds
(150K, Plain TeX)

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.