L Turban 1991 J. Phys. A: Math. Gen. 24 L1119 doi:10.1088/0305-4470/24/18/009
L Turban
Show affiliationsThe statistics of nested spiral, self-avoiding 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 cN approximately=(square root 2/24)N-3/2 exp(pi square root 2/3 N1/2) and their average size XN approximately=(1/2 pi ) square root 3/2 N1/2 ln N to leading order on the square lattice while the corresponding values for the triangular lattice are cN approximately= (33/4/16) N-5/4 exp(( pi/square root 3) N1/2) and XN approximately= 1/(pi square root 3) N1/2 ln N.
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
Issue 18 (21 September 1991)
L Turban 1991 J. Phys. A: Math. Gen. 24 L1119
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M A Fortes and P I C Teixeira 2003 J. Phys. A: Math. Gen. 36 5161
Antonio Padilla 2004 Class. Quantum Grav. 21 2899
Jeffrey D Martin and Steven D Hudson 2009 New J. Phys. 11 115005
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