  The paper continues the development of the rigorous supersymmetric transfer
matrix approach to the random band matrices started in J Stat Phys 164:1233 --
1260, 2016; Commun Math Phys 351:1009 -- 1044, 2017. We consider random
Hermitian block band matrices consisting of $W\times W$ random Gaussian blocks
(parametrized by $j,k \in\Lambda=[1,n]^d\cap \mathbb{Z}^d$) with a fixed
entry's variance $J_{jk}=\delta_{j,k}W^{-1}+\beta\Delta_{j,k}W^{-2}$, $\beta>0$
in each block. Taking the limit $W\to\infty$ with fixed $n$ and $\beta$, we
derive the sigma-model approximation of the second correlation function similar
to Efetov's one. Then, considering the limit $\beta, n\to\infty$, we prove that
in the dimension $d=1$ the behaviour of the sigma-model approximation in the
bulk of the spectrum, as $\beta\gg n$, is determined by the classical Wigner --
Dyson statistics.
