Polymers in a random environment

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Abstract
Self-avoiding polymer chains in a random environment are considered by means of the renormalization group (RG) and without using the replica trick. The coupled differential equations of the RG for the excluded volume strength and for the strength of the disorder are derived and solved up to the first order of in =4-d. The quenched average of the number of states of a polymer chain is studied. In the case of finite volume the result obtained is in agreement with that derived earlier by Machta (1989). The radius of the collapsed polymer derived by Edwards and Muthukumar (1988) is rederived within the RG method. The quenched average of the second viral coefficient of a solution of polymers in the random environment is considered.