We present the results of a new perturbation calculation in polymer statistics which starts from a ground state that already correctly predicts the long chain length behaviour of the mean square end‐to‐end distance 〈R2N〉, namely, the solution to the two dimensional (2D) Edwards model. The 〈R2N〉 thus calculated is shown to be convergent in N, the number of steps in the chain, in contrast to previous methods which start from the free random walk solution. This allows us to calculate a new value for the leading correction‐to‐scaling exponent Δ. Writing 〈R2N〉=AN2ν(1+BN−Δ+CN−1+...), where ν=3/4 in 2D, our result shows that Δ=1/2. This value is also supported by an analysis of 2D self‐avoiding walks on the continuum.
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This statement requires the approximate equality of the exact amplitudes, and , as clearly the “perturbative” (i.e., approximate) amplitudes cancel by virtue of the convergence of Eq. (39) and its 3D equivalent. We are unfortunately not able to prove this at present.
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© 1996 American Institute of Physics.
1996
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