A pr 1 99 9 Effective - field approximations , including DMRG method , for classical inhomogeneous 2 D spin lattice models

A new approach to derivation of various effective-field approximations for lattice spin models in a unique way 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 spin renormal-ization, is derived, yielding results practically not different from the DMRG ones. The matrix-product wave function of Rommer and¨Ostlund can be constructed from the output of the method. The computational costs of all the derived methods are smaller than those of the DMRG. Most of the results are applicable to the 1D quantum systems, as well.