The transfer matrix approach to the self-avoiding walk in fractal spaces

Xiang Rong Wang

Physica A: Statistical Mechanics and its Applications, 1994, vol. 205, issue 1, 391-398

Abstract: The random walk and the self-avoiding walk in finitely ramified fractal spaces have been studied. The exact values of size exponents v of the random walk and the self-avoiding walk on the modified Koch fractal with loops and the Sierpinski gasket are obtained from the transfer matrix method. We find v=ln(3)ln(403) and v=ln(2)ln(5) for the random walk, and v=0.877 and v=0.785 for the self-avoiding walk on the Koch fractal and the Sierpinski gasket, respectively. The values for the self-avoiding walk are different from those obtained from the conventional renormalization group calculations.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:205:y:1994:i:1:p:391-398

DOI: 10.1016/0378-4371(94)90517-7

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