Abstract
We consider the statistical mechanics of a fluctuating string (1D solid-on-solid model) ofN columns with a contact energy term displaying a critical wetting transition. For this model we derive a contour integral representation for the finite-size partition function. From this representation we derive a polynomial representation and obtain the Lee-Yang zeros forN ≲, 100. Through the asymptotic evaluation of the contour integral we evaluate the zeros for higherN. This asymptotic evaluation displays a Stokes phenomenon providing a different viewpoint of the mechanism by which a phase transition can arise, supplementing the picture of Lee and Yang. We also reproduce and extend somewhat the results of Smith for the finite-size scaling limit of the partition function.
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Pisani, C., Smith, E.R. Lee-Yang zeros and stokes phenomenon in a model with a wetting transition. J Stat Phys 72, 51–78 (1993). https://doi.org/10.1007/BF01048040
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DOI: https://doi.org/10.1007/BF01048040