Comprehensive mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model

We present an unbiased mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model on a square lattice, both at zero and finite temperatures. Unrestricted Hartree-Fock calculations on large finite lattices are complemented by solutions restricted to N\'eel and circular spiral order in the thermodynamic limit. The magnetic states are classified by a systematic scheme based on the dominant Fourier components of the spin texture. On finite lattices a whole zoo of ordering patterns appears. We show that many of these states are finite size artifacts related to the limited choice of ordering wave vectors on a finite lattice. In the thermodynamic limit only three classes of states with a relatively simple structure survive: N\'eel, circular spiral, and stripe states. Stripes involve also charge order and can be unidirectional or bidirectional, with horizontal and/or vertical orientation. We present complete phase diagrams in the plane spanned by electron density and temperature, for a moderate Hubbard interaction and various choices of the next-nearest neighbor hopping amplitude.