https://doi.org/10.1007/s100510050727
On the 1/D expansion for directed polymers
1
Dip. di Fisica, I Università di Roma "La Sapienza",
Piazzale Aldo Moro, 00185 Roma,
Italy
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
