Canonical chain growth with PERM

Scaling of mean square radius of gyration and end-to-end distance for self-avoiding walks. Data points refer to results from PERM runs for W = 16,32. 32 768 steps. Lines manifest the respective power-law behaviors. 

Monte Carlo and chain growth methods for molecular simulations 

The main difference in comparison with the original PERM is that, if the sample of chains of length n — 1 shall be enriched, the continuations to an unoccupied nearest-neighbor site have to be different, i.e., the weights of these chains with length n can differ. Therefore it is impossible to calculate a uniform weight like as given in Eq. (4.146) 

Considering the probabilities px as partial intervals of certain length, arranging them successively in the total interval [0,1] (since Y1aPx = 1) and drawing a random number re [0,1), one selects the tuple whose interval contains r. This tuple of different sites is then chosen to continue the chain. The corresponding weights are [38]  

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