Statistical mechanics of self-avoiding tethered manifolds

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Abstract
A formalism which allows perturbative renormalization-group calculations for self-avoiding polymers and flexible membranes of a fixed internal connectivity is presented in detail. Upon considering general D-dimensional elastic manifolds embedded in a d-dimensional space, we expand about a line in the (d,D) plane separating ideal ‘‘phantom manifold’’ behavior from a region where self-avoiding interactions are important. When d is fixed at 3, this procedure leads to a (6/7+ε expansion for the radius of gyration exponent ν, where ε=D-(6/7. Although we obtain consistent results for ν to lowest order in ε, the generalized polymer exponent γ displays an anomalous dependence on the shape of the manifold boundary.

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