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Generalized mean-field approximations, including DMRG method, for classical inhomogeneous 2D spin lattice models

A new approach to derivation of generalized mean-field approximations for lattice spin models is presented. It is shown that it can give a number of methods, including the DMRG method, that can be used to find generally inhomogeneous solutions of 2D classical lattice problems. A method, closely related to the DMRG method but without necessity to perform any renormalization, is derived, yielding results practically not different from the DMRG ones. The computational costs of all the derived methods are smaller than those of the DMRG. All the results are applicable to the 1D quantum systems, as well.