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The trail problem on the square lattice

A Malakis

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The trail problem on the square lattice is studied by the method of exact enumeration and its relation to the self-avoiding walk problem is pointed out. The number of N-stepped trails and their mean-square sizes are enumerated on a computer up to N=17. An asymptotic analysis of the numerical data suggests that certain critical exponents obey the same values for both the trail and the self-avoiding walk problem on the square lattice.


PACS

05.50.+q Lattice theory and statistics (Ising, Potts, etc.)

05.40.Fb Random walks and Levy flights

MSC

82B27 Critical phenomena

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)

Subjects

Statistical physics and nonlinear systems

Dates

Issue 8 (August 1976)



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