Statistics of nested spiral selfavoiding loops: exact results on the square and triangular lattices
Abstract
The statistics of nested spiral, selfavoiding loops, which is closely related to the partition of integers into decreasing parts, has been studied on the square and triangular lattices. The number of configurations with N steps is c_{N} approximately=(2/24)N^{3}2/ exp( pi 2/3 N^{1}2/) and their average size X_{N} approximately=(1/2 pi )3/2 N^{1}2/ 1n N to leading order on the square lattice while the corresponding values for the triangular lattice are c_{N} approximately=(3^{3}4//16) N^{5}4/ exp(( pi /3) N^{1}2/) and X_{N} approximately=1/( pi 3)N^{1}2/ 1n N.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 September 1991
 DOI:
 10.1088/03054470/24/18/009
 Bibcode:
 1991JPhA...24L1119T