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Quantum critical points exist at zero temperature, yet, experimentally theirinfluence seems to extend over a large part of the phase diagram of systemssuch as heavy-fermion compounds and high-temperature superconductors.Theoretically, however, it is generally not known over what range of parametersthe physics is governed by the quantum critical point. We answer this questionfor the spin-density wave to fermi-liquid quantum critical point in thetwo-dimensional Hubbard model. This problem is in the $d=2,z=2$ universalityclass. We use the Two-Particle Self-Consistent approach, which is accurate fromweak to intermediate coupling, and whose critical behavior is the same as forthe self-consistent-renormalized approach of Moriya. Despite the presence oflogarithmic corrections, numerical results demonstrate that quantum criticalscaling for the static magnetic susceptibility can extend up to very hightemperatures but that the commensurate to incommensurate crossover leads todeviations to scaling.

Scaling and commensurate-incommensurate crossover for the d=2, z=2 quantum critical point of itinerant antiferromagnets