Abstract
An infinity of exact critical exponents for two-dimensional self-avoiding walks can be derived from conformai invariance and Coulomb gas techniques applied to the O(n) model and to the Potts model. They apply to polymer networks of any topology, for which a general scaling theory is given, valid in any dimension d. The infinite set of exponents has also been calculated to O(ε2), for d=4-ε. The 2D study also includes other universality classes like the dense polymers, the Hamiltonian walks, the polymers at their ω-point. Exact correlation functions can be further given for Hamiltonian walks, and exact winding angle probability distributions for the self-avoiding walks.
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Duplantier, B. (1988). Exact Critical Properties of Two-Dimensional Polymer Networks from Conformal Invariance. In: Jullien, R., Peliti, L., Rammal, R., Boccara, N. (eds) Universalities in Condensed Matter. Springer Proceedings in Physics, vol 32. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51005-2_13
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DOI: https://doi.org/10.1007/978-3-642-51005-2_13
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