On the 1/D expansion for directed polymers
Dip. di Fisica, I Università di Roma "La Sapienza",
Piazzale Aldo Moro, 00185 Roma,
2 Center for Theoretical Study, Jilská 1, 11000 Praha, Czech Republic
We present a variational approach for directed polymers in D transversal dimensions which is used to compute the correction 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-D 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.
PACS: 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999