E W James and C E Soteros 2007 J. Phys. A: Math. Theor. 40 14945 doi:10.1088/1751-8113/40/50/003
E W James1 and C E Soteros2
Show affiliationsA trail on the square lattice with a fixed number, k, of vertices of degree 4 is called a k-trail. We model polymer collapse using k-trails by incorporating an interaction energy which is proportional to the number of nearest-neighbour contact edges of the trail. It is known that the number of square lattice n-edge closed (open) k-trails can be bounded above and below (to O(nk)) by the number of n-step self-avoiding circuits (walks). This along with pattern theorems for self-interacting self-avoiding circuits and walks are used herein to establish upper and lower bounds (to O(nk)) for the collapsing free energy of k-trails in terms of self-avoiding circuits or walks, as appropriate. We also use pattern theorems to obtain bounds on the limiting nearest-neighbour contact density for collapsing k-trails. Finally, we investigate k-trails with a fixed density of nearest-neighbour contacts and show that their limiting entropy per monomer is independent of k.
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
05.40.Fb Random walks and Levy flights
61.25.H- Macromolecular and polymers solutions; polymer melts
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
Issue 50 (14 December 2007)
Received 1 September 2007, in final form 24 October 2007
Published 28 November 2007
E W James and C E Soteros 2007 J. Phys. A: Math. Theor. 40 14945
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