Temperature dependence of antiferromagnetic order in the Hubbard model

We suggest a method for an approximative solution of the two dimensional Hubbard model close to half filling. It is based on partial bosonisation, supplemented by an investigation of the functional renormalisation group flow. The inclusion of both the fermionic and bosonic fluctuations leads in lowest order to agreement with the Hartree-Fock result or Schwinger-Dyson equation and cures the ambiguity of mean field theory . We compute the temperature dependence of the antiferromagnetic order parameter and the gap below the critical temperature. We argue that the Mermin-Wagner theorem is not practically applicable for the spontaneous breaking of the continuous spin symmetry in the antiferromagnetic state of the Hubbard model. The long distance behavior close to and below the critical temperature is governed by the renormalisation flow for the effective interactions of composite Goldstone bosons and deviates strongly from the Hartree-Fock result.Comment: New section on critical behavior 31 pages,17 figure

Antiferromagnetic gap in the Hubbard model

We compute the temperature dependence of the antiferromagnetic order parameter and the gap in the two dimensional Hubbard model at and close to half filling. Our approach is based on truncations of an exact functional renormalization group equation. The explicit use of composite bosonic degrees of freedom permits a direct investigation of the ordered low temperature phase. We show that the Mermin--Wagner theorem is not practically applicable for the spontaneous breaking of the continuous spin symmetry in the antiferromagnetic state. The critical behavior is dominated by the fluctuations of composite Goldstone bosons.Comment: new discussion of critical behavior 4 pages,2 figures, LaTe

Spontaneous symmetry breaking in the colored Hubbard model

The Hubbard model is reformulated in terms of different ``colored'' fermion species for the electrons or holes at different lattice sites. Antiferromagnetic ordering or d-wave superconductivity can then be described in terms of translationally invariant expectation values for colored composite scalar fields. A suitable mean field approximation for the two dimensional colored Hubbard model shows indeed phases with antiferromagnetic ordering or d-wave superconductivity at low temperature. At low enough temperature the transition to the antiferromagnetic phase is of first order. The present formulation also allows an easy extension to more complicated microscopic interactions.Comment: 19 pages, 5 figure