Yohannes Shiferaw and Yadin Y Goldschmidt 2000 J. Phys. A: Math. Gen. 33 4461 doi:10.1088/0305-4470/33/24/305
Yohannes Shiferaw and Yadin Y Goldschmidt
Show affiliationsWe 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 behaviour 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 R2~L, where R is the end-to-end distance and L is the number of links, whereas for a chain anchored at one end R2~L4. The exact results are found to agree with an alternative numerical solution in d = 1 dimensions. The crossover from long-range to short-range correlations of the disorder is also explored.
05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
02.50.-r Probability theory, stochastic processes, and statistics
82D30 Random media, disordered materials (including liquid crystals and spin glasses)
Issue 24 (23 June 2000)
Received 8 March 2000, in final form 8 May 2000
Yohannes Shiferaw and Yadin Y Goldschmidt 2000 J. Phys. A: Math. Gen. 33 4461
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