On the 1/D expansion for directed polymers
arXiv:cond-mat/9712208
Abstract
We present a variational approach for directed polymers in transversal dimensions which is used to compute the corrections to the mean field theory predictions with broken replica symmetry. The trial function is taken to be a symmetrized version of the mean-field solution, which is known to be exact for . We compute the free energy corresponding to that function and show that the finite- corrections behave like . It means that the expansion in powers of 1/D should be used with great care here. We hope that the techniques developed in this note will be useful also in the study of spin glasses.
Latex, 16 pages, 3 figures