05-20U

At the change of temperature or under the action of external parameters crystalline surfaces can undergo phase transitions. In present paper the works considering the discrete lattice models are examined. The advantage of discrete lattice models is a possibility to describe the flat, rough, reconstructed and disordered flat phases. The special attention is devoted to the transfer-matrix method which permits to reduce the study of temperature behavior of SOS models to the ground-state problem of one-dimensional quantum systems. The order parameters for the surface and quantum spin chains phases are compared; a correspondence between the asymptotic of height-height correlations functions and spin correlation functions is set.