S G Whittington and A J Guttmann 1990 J. Phys. A: Math. Gen. 23 5601 doi:10.1088/0305-4470/23/23/030
Self-avoiding walks which cross a square
S G Whittington and A J Guttmann
Show affiliationsThe authors consider self-avoiding walks on the square lattice which are confined to lie in or on the boundary of a square with vertices at (0, 0), (0, L), (L, 0) and (L, L). They ask for the number of such walks which begin at the origin and end at the vertex (L, L), especially in the large L limit. Similarly they ask for the mean number of steps in such walks as a function of L. At fixed L the authors also associate a fugacity with the number of steps of the walk and ask how the system behaves as a function of this fugacity. They provide some rigorous results, in particular proving that there is a phase transition at some particular value of the fugacity, and supplement these with the analysis of series data for the problem.
- PACS
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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
05.70.Fh Phase transitions: general studies
- MSC
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82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B26 Phase transitions (general)
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
- Subjects
- Dates
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Issue 23 (7 December 1990)
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Self-avoiding walks which cross a square
S G Whittington and A J Guttmann 1990 J. Phys. A: Math. Gen. 23 5601
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