Abstract
We obtain the generating function for an ensemble of random walkers on the Cayley tree of coordination numberz. The pair interaction between walkers is taken into account. This forbids two walkers to occupy the same lattice point after an equal number of steps. Interacting polymer statistics results from this model if one associates time (or the number of steps) with an additional space coordinate. The limiting free energy appears in a form that corresponds to the phase transition of “3/2 order.”
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Priezzhev, V.B. Interacting walkers on the Cayley tree, and polymer statistics. J Stat Phys 44, 921–932 (1986). https://doi.org/10.1007/BF01011914
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DOI: https://doi.org/10.1007/BF01011914