08-12U

In the paper the BCSOS model of a surface and its generalization for the case of further interactions and for the case of the two-component surface is considered. Using the transfer-matrix method the problem is reduced to the study of the ground state of one-dimensional quantum spin models. It is shown that further than the nearest neighbor interactions may lead to the appearance of competing interactions in a quantum chain, whereas for the two-component surface the correspondence to the periodic quantum chain has been found. The possibility of the description of the GaAs surface within the mentioned models has been also analyzed.