Large N Expansion for 4-Epsilon Dimensional Oriented Manifolds in Random Media

Details Large N Expansion for 4-Epsilon Dimensional Oriented Manifolds in Random Media Large N Expansion for 4-Epsilon Dimensional Oriented Manifolds in Random Media

1993-03-25

arxiv.org/abs/cond-mat/9303046v1

Physics

Condensed Matter

23 pages + 4 figures available upon request, Plain TeX

Scientific paper

10.1103/PhysRevB.48.5949

The equilibrium statistical mechanics of a d dimensional ``oriented'' manifold in an N+d dimensional random medium are analyzed in d=4-epsilon dimensions. For N=1, this problem describes an interface pinned by impurities. For d=1, the model becomes identical to the directed polymer in a random medium. Here, we generalize the functional renormalization group method used previously to study the interface problem, and extract the behavior in the double limit epsilon small and N large, finding non-analytic corrections in 1/N. For short-range disorder, the interface width scales as a power law of the width. We calculate the roughness exponent characterizing this power law for small epsilon and large N, as well as other properties of the phase. We also analyze the behavior for disorder with long-range correlations, as is appropriate for interfaces in random field systems, and study the crossover between the two regimes.

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