Skeleton expansions for directed polymers in disordered media
| dc.creator | Stepanow, Semjon | |
| dc.date | 2007-09-30 | |
| dc.date.accessioned | 2026-07-07T08:33:08Z | |
| dc.date.available | 2026-07-07T08:33:08Z | |
| dc.description | Partial summations of perturbation expansions of the directed polymer in disordered media (DPRM) enables one to represent the latter as skeleton expansions in powers of the effective coupling constant $Δ(t)$, which corresponds to the binding state between two replicas in the replica field theory of DPRM, and is equivalent to the binding state of a quantum particle in an external $δ$% -potential. The strong coupling phase is characterized by the exponential dependence of $Δ(t)$ on $t$, $Δ(t)\sim \exp (p_{c}t)$ with $% p_{c} $ being the binding energy of the particle. For dimensions $d>2$ the strong coupling phase exists for $Δ_{0}>Δ_{c}(d)$. We compute explicitly the mean-square displacement and the 2nd cumulant of the free energy to the lowest order in powers of effective coupling in $d=1$. We argue that the elimination of the terms $\exp (p_{c}t)$ in skeleton expansions demands an additional partial summation of skeleton series. | |
| dc.description | 4 pages, 5 figures | |
| dc.identifier | https://arxiv.org/abs/0710.0081 | |
| dc.identifier | http://arxiv.org/abs/0710.0081 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139022 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Skeleton expansions for directed polymers in disordered media | |
| dc.type | text |