Incommensurate structures studied by a modified density-matrix renormalization-group method

A modified density-matrix renormalization-group (DMRG) method is introduced and applied to classical two-dimensional models: the anisotropic triangular nearest-neighbor Ising model and the anisotropic triangular next-nearest-neighbor using model. Phase diagrams of both models have complex structures and exhibit incommensurate phases. It was found that the incommensurate phase completely separates the disordered phase from one of the commensurate phases, i.e., the nonexistence of the Lifshitz paint is conjectured in phase diagrams of both models with the DMRG method. It is shown that the DMRG method is also an effective-field approximation, but in spite of that it yields the correct value of the domain wall density critical exponent.