Owczarek, A L, Essam, J W and Brak, R (2001) Scaling analysis for the adsorption transition in a watermelon network of n directed non-intersecting walks. Journal of Statistical Physics, 102 (3-4).
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The partition function for the problem of n directed non-intersecting walks interacting via contact potentials with a wall parallel to the direction of the walks has previously been calculated as an n by n determinant. Here, we describe how to analyse the scaling behaviour of this problem using alternative representations of the solution. In doing so we derive the asymptotics of the partition function of a watermelon network of n such walks for all tem- peratures, and so calculate the associated network exponents in the three regimes: desorbed, adsorbed, and at the adsorption transition. Furthermore, we derive the full scaling function around the adsorption transition for all n. At the adsorption transition we also derive a simple "product form" for the partition function. These results have, in part, been derived using recurrence relations satised by the original determinantal solution.
This is a Published version This version's date is: 02/2001 This item is peer reviewed
https://repository.royalholloway.ac.uk/items/2b26113b-6189-b72f-816a-bf440aec6466/1/
Deposited by () on 23-Dec-2009 in Royal Holloway Research Online.Last modified on 23-Dec-2009
E-print is the authors' final version.
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