Spin disorder in the two-dimensional Hubbard model: A mean-field theory

A scheme of symmetry breaking is proposed for the two-dimensional Hubbard model at less than half filling. The self-induced mean field is a random spin-dependent potential. The energy of the spin-disordered state is shown to be lower than that of commensurate or incommensurate antiferromagnetic states. Long-wavelength charge and spin fluctuations obey the diffusion equation, leading to deviations from Fermi-liquid behavior. At wave vector q=(π,π) the transverse spin-excitation spectrum has a gap.