• DOI:10.1142/9789812565518_0009
• Corpus ID: 119669505

Statistical Mechanics of Self-Avoiding Manifolds (Part II)

@article{Duplantier2004StatisticalMO,
  title={Statistical Mechanics of Self-Avoiding Manifolds (Part II)},
  author={Bertrand Duplantier},
  journal={arXiv: Statistical Mechanics},
  year={2004}
}

• B. Duplantier
• Published 18 August 2004
• Mathematics
• arXiv: Statistical Mechanics

We consider a model of a D-dimensional tethered manifold interacting by excluded volume in R^d with a single point. Use of intrinsic distance geometry provides a rigorous definition of the analytic continuation of the perturbative expansion for arbitrary D, 0 < D < 2. Its one-loop renormalizability is first established by direct resummation. A renormalization operation R is then described, which ensures renormalizability to all orders. The similar question of the renormalizability of the self-avoiding manifold (SAM) Edwards model is then considered, first at one-loop, then to all orders. We describe a short-distance multi-local operator product expansion, which extends methods of local field theories to a large class of models with non-local singular interactions. It vindicates the direct renormalization method used earlier in part I of these lectures, as well as the corresponding scaling laws.