Temperature dependence of antiferromagnetic order in the Hubbard model

The authors suggest an approximative solution of the two-dimensional Hubbard model close to half-filling. It is based on partial bosonization, supplemented by an investigation of the functional renormalization group flow. The inclusion of the fermionic and bosonic fluctuations leads in lowest order to agreement with Hartree-Fock result or Schwinger-Dyson equation and cures the mean field ambiguity. 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 renormalization flow for the effective interactions of composite Goldstone bosons and deviates strongly from the Hartree-Fock result.