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Low-Energy Excitations in an Incipient Antiferromagnet

We present fully self-consistent calculations in the fluctuation exchange approximation for the half-filled Hubbard model in 2D. A non-fermi liquid state evolves with decreasing temperature in this self-consistent model of coupled spin fluctuations and quasiparticles. The mean field phase transition to long-range antiferromagnetic order is suppressed and we find no evidence of a phase transition to long-range magnetic order. We show that the real part of the self-energy at zero energy shows a positive slope and the imaginary part of the self-energy shows a local minimum. The scale of this structure is set by the zero temperature gap in mean field theory. The growth of spin fluctuations is reflected in the evolution of sharply peaked structure in the spin fluctuation propagator around zero energy and ${\bf Q} = (π, π)$. We present calculations for the Hubbard model in 1D in a two-particle self-consistent parquet approximation. A second moment sum rule suggests that vertex corrections to the self-energy are responsible for the greater accuracy of the parquet approximation as compared to other self-consistent perturbation theories.