Incommensurate and Commensurate Density-Wave in the Two-Dimensional Lattice

We have investigated anisotropic density-wave phase with arbitrary ordering wave vector (Q) and estimated the value of Q that corresponds to the minimum of the free energy. We have found that for a wide range of model parameters the commensurate d-density-wave (DDW) is actually the most stable density-wave state. However, for moderate doping the commensurate DDW state is stable only at finite temperatures and disappears when the temperature is sufficiently low. These features may assist in clarification of the mechanism of the pseudogap.