Strong-interaction approximation for transfer matrix method

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.