Resistance and related scaling properties of self-avoiding random walks

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Abstract
Three scaling exponents for random and self-avoiding chains are studied by direct renormalisation. These describe the end-to-end resistance of a conducting chain; the arc length of the shortest path traceable between the chain ends; and the arc length of chain in no loop. The scaling behaviours of these quantities are identical to first order in epsilon =4-d. (d is the space dimension). For a long self-avoiding chain, the authors predict that each one one is proportional to the chain length.