Shortest path of SAWs with bridges: series results

Barat, K. ; Karmakar, S. N. ; Chakrabarti, B. K. (1990) Shortest path of SAWs with bridges: series results Journal of Physics A: Mathematical and General, 23 (11). pp. 2217-2222. ISSN 0305-4470

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Recent Monte Carlo simulation results of Yang and Chakrabarti (1990) suggest that the shortest path SN of an N-stepped self-avoiding walk (SAW), with finite range interactions of bridges, has a finite size scaling behaviour SN/N approximately=A+N- δ (B+C/N), where the exponent δ is superuniversal; δ approximately=0.19 for all dimensions δ studied (2<or=δ<or=5). The authors report the small-N series enumeration results for SN for SAWs with nearest-neighbour bridges on square (up to N=18), triangular (up to N=11) and simple cubic (up to N=12) lattices. The estimated values of Delta for different lattices (approximately=0.22+or−0.01 for d=2 and approximately=0.26+or−0.01 for d=3) have been compared with the above Monte Carlo estimate and the indication of a superuniversal behaviour for δ has been discussed.

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