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金沢工業大学研究紀要 A

Absence of Ferromagnetism or Antiferromagnetism in the One- and Two-Dimensional Extended Hubbard Models

Akiomi Mishima

Published Jan 1, 1978• 0 citations
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It is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-SSS Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in one and two dimensions.
A numerical scaling analysis is used to show that Nagaoka's ferromagnetic state in the two-dimensional Hubbard model with one hole is superseded by an antiferromagnetic (AF) state with a discontinuous jump in the total spin due to the AF coupling as the Hubbard U is made finite. The same applies to the two-hole system, which has a spiral spin structure. We can show, via the scaling, that the crossover to an AF state is a precursor of a pathological coalescence of states having the minimum spin and Nagaoka's state at U=\ensuremath{\infty} in the thermodynamic limit.