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- W1984521074 abstract "We consider the mathematical properties of the generating and partition functions in the two-variable scaling region about the tricritical point in some models of polymer collapse. We concentrate on models that have a similar behaviour to that of interacting partially-directed self-avoiding walks (IPDSAW) in two dimensions. However, we do not restrict the discussion to that model. After describing the properties for a general class of models, and stating exactly what we mean by scaling, we prove the following theorem: If the generating function of finite-size partition functions has a tricritical cross-over scaling form around the theta -point, and the associated tricritical scaling function, g, has a finite radius of convergence, then the partition function has a finite-size scaling form and importantly the finite-size scaling function, f, is an entire function. In the IPDSAW case we have an explicit representation of the finite-size scaling function. We point out that given our description of tricritical scaling this theorem should apply mutatis mutandis to a wider class of theta -point models. We discuss the result in relation to the Edwards model of polymer collapse for which it has recently been argued that the finite-size scaling functions are not entire." @default.
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- W1984521074 date "1995-09-07" @default.
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- W1984521074 title "On the analyticity properties of scaling functions in models of polymer collapse" @default.
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- W1984521074 doi "https://doi.org/10.1088/0305-4470/28/17/007" @default.
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