  Using transfer-matrix method a correspondence between $2D$ classical spin
systems ($2D$ Ising model and six-vertex model) and $1D$ quantum spin systems
is considered. We find the transfer matrix in two limits - in a well-known
strong-anisotropy limit and a novel strong-interaction limit. In contrast to
the usual strong-anisotropy approximation, within the strong-interaction
approximation we take into account the non-commutativity of transfer-matrix
components. The latter approximation is valid for low temperatures or strong
interaction in one spatial dimension. We observe that the Hamiltonian of the
corresponding quantum chains contains multispin interactions.
