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- W2147035472 abstract "An adsorbing directed path in a half-space is a model of a dilute polymer adsorbing onto a hard wall. The simplest adsorbing directed path is the adsorbing Dyck path, and it is a two-dimensional path in the positive half-space in the square lattice. This model is known to have a continuous phase transition where the path adsorbs onto the X axis (which is the adsorbing line). In this paper I generalize this model slightly by lifting the endpoints of the path from the adsorbing line. I determine the limiting free energy of directed paths with lifted endpoints and show that the general model has a first-order adsorption transition which reduces to a continuous adsorption transition in special cases when either one or both endpoints of the path are fixed in the adsorbing line. In addition, the partition function of this model is examined and non-exact asymptotic formulae are determined which exhibit critical scaling around the continuous critical point." @default.
- W2147035472 created "2016-06-24" @default.
- W2147035472 creator A5052790968 @default.
- W2147035472 date "2010-08-31" @default.
- W2147035472 modified "2023-09-23" @default.
- W2147035472 title "The adsorption transition in directed paths" @default.
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- W2147035472 doi "https://doi.org/10.1088/1742-5468/2010/08/p08030" @default.
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