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A note on mean-field behavior for self-avoiding walk on branching planes

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Abstract

We consider the critical behavior of the susceptibility of the self-avoiding walk on the graphT×Z, whereT is a Bethe lattice with degreek andZ is the one dimensional lattice. By directly estimating the two-point function using a method of Grimmett and Newman, we show that the bubble condition is satisfied whenk>2, and therefore the critical exponent associated with the susceptibility equals 1.

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Authors and Affiliations

  1. Department of Mathematics, Penn State University, Beaver Campus, 15061, Monaca, Pennsylvania

    C. Chris Wu

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  1. C. Chris Wu
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Wu, C.C. A note on mean-field behavior for self-avoiding walk on branching planes. J Stat Phys 81, 673–680 (1995). https://doi.org/10.1007/BF02179252

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  • DOI: https://doi.org/10.1007/BF02179252

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