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Renormalization theory of self-avoiding walks which cross a square

Prentis, J. J.

Prentis, J. J.

1991-11-07

Citation:Prentis, J J (1991). "Renormalization theory of self-avoiding walks which cross a square." Journal of Physics A: Mathematical and General. 24(21): 5097-5103. <http://hdl.handle.net/2027.42/48825>

Abstract: The renormalization group theory is used to calculate the critical behaviour of self-avoiding walks which cross a square. This problem, which has been proposed recently, is especially well suited for a renormalization group analysis. The fixed-endpoint, diagonal-span trademark of the square-crossing walks leads naturally to a well defined renormalization scheme. Unlike other finite-lattice renormalization schemes for self-avoiding walks, this square-crossing renormalization is exact in the sense that the finite lattice (square) is uniquely defined, the spanning rule is unambiguous, and the end-to-end correlations are exactly preserved. The results for the critical point are in excellent agreement with series analysis estimates and support a conjecture on its exact value.