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Interacting Crumpled Manifolds: Exact Results to all Orders of Perturbation Theory

Henryk A. Pinnow·Kay Joerg Wiese
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Abstract

In this letter, we report progress on the field theory of polymerized tethered membranes. For the toy-model of a manifold repelled by a single point, we are able to sum the perturbation expansion in the strength g of the interaction exactly in the limit of internal dimension D -> 2. This exact solution is the starting point for an expansion in 2-D, which aims at connecting to the well studied case of polymers (D=1). We here give results to order (2-D)^4, where again all orders in g are resummed. This is a first step towards a more complete solution of the self-avoiding manifold problem, which might also prove valuable for polymers.

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Henryk A. Pinnow, Kay Joerg Wiese. 2002-09-30. Interacting Crumpled Manifolds: Exact Results to all Orders of Perturbation Theory. https://doi.org/10.1209/epl%2Fi2003-00204-2

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