A disorder-dependent Gaussian variational approach is applied to the problem of a d-dimensional polymer chain in a random medium (or potential). Two classes of variational solutions are obtained. For d<2, these two classes may be interpreted as domain and domain-wall. The critical exponent ν describing the polymer width is ν=1/(4-d) (domain solution) or ν=3/(d+4) (domain-wall solution). The domain-wall solution is equivalent to the (full) replica symmetry-breaking variational result. For d>2, we find ν=. No evidence of a phase transition is found for 24, the other variational solution undergoes a phase transition, which has some similarity with Derrida's random energy models.

• Received 29 March 1996

DOI:https://doi.org/10.1103/PhysRevB.55.226