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Exact fractal dimension of the loop-erased self-avoiding walk in two dimensions.

The fractal dimension of the loop-erased self-avoiding walk is shown to be identical to that of the chemical path on equally likely spanning trees. This result is valid for arbitrary lattices and in all dimensions. In particular, in two dimensions, using the spanning tree correspondence and the known results for the Potts model from conformal field theory, the fractal dimension is shown to be exactly 5/4 as conjectured by Guttmann and Bursill