Frustration of antiferromagnetism in the t-t′-Hubbard model at weak coupling



The perfect-nesting instability towards antiferromagnetism of the Hubbard model is suppressed by next-nearest neighbor hopping t′. The asymptotic behavior of the critical coupling Ut (t′) at small t′ is calculated in dimensions d = 2,3, ∞ using Hartree theory; this yields the exact result at least in d >> 2. The order of the transition is also determined. A region of stability of a metallic antiferromagnetic phase in d = 3 is identified.