2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139022Partial 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.4 pages, 5 figuresStatistical MechanicsDisordered Systems and Neural Networkstext