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Solvable model of a polymer in random media with long ranged disorder correlations

Yohannes Shiferaw·Yadin Y. Goldschmidt
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Abstract

We present an exactly solvable model of a Gaussian (flexible) polymer chain in a quenched random medium. This is the case when the random medium obeys very long range quadratic correlations. The model is solved in $d$ spatial dimensions using the replica method, and practically all the physical properties of the chain can be found. In particular the difference between the behavior of a chain that is free to move and a chain with one end fixed is elucidated. The interesting finding is that a chain that is free to move in a quadratically correlated random potential behaves like a free chain with $R^2 \sim L$, where $R$ is the end to end distance and $L$ is the length of the chain, whereas for a chain anchored at one end $R^2 \sim L^4$. The exact results are found to agree with an alternative numerical solution in $d=1$ dimensions. The crossover from long ranged to short ranged correlations of the disorder is also explored.

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Yohannes Shiferaw, Yadin Y. Goldschmidt. 2000-03-08. Solvable model of a polymer in random media with long ranged disorder correlations. https://doi.org/10.1088/0305-4470%2F33%2F24%2F305

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