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- W2279009121 abstract "We consider a model for a directed polymer in a random environment defined on a hierarchical diamond lattice in which i.i.d. random variables are attached to the lattice bonds. Our focus is on scaling schemes in which a size parameter $n$, counting the number of hierarchical layers of the system, becomes large as the inverse temperature $beta$ vanishes. When $beta$ has the form $widehat{beta}/sqrt{n}$ for a parameter $widehat{beta}>0$, we show that there is a cutoff value $0 kappa $. We obtain a more refined description of the border between these two regimes by setting the inverse temperature to $kappa/sqrt{n} + alpha_n$ where $0 eta$. Extending the analysis yet again by probing around the inverse temperature $kappa/sqrt{n} + eta (log n-log log n)/n^{3/2}$ we find an infinite sequence of nested critical points for the variance behavior of the normalized partition function. In the subcritical cases $widehat{beta} leq kappa$ and $alpha leq eta$ this analysis is extended to a central limit theorem result for the fluctuations of the normalized partition function." @default.
- W2279009121 created "2016-06-24" @default.
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- W2279009121 date "2016-02-22" @default.
- W2279009121 modified "2023-09-27" @default.
- W2279009121 title "Nested critical points for a directed polymer on a disordered diamond lattice" @default.
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