Temperature dependence of antiferromagnetic order in the Hubbard model

Physical Review B - Condensed Matter and Materials Physics

Volumn 70, Issue 12, 2004, Pages

  Baier, Tobias ^a   Bick, Eike ^a   Wetterich, Christof ^a  

^a INSTITUT FÜR THEORETISCHE PHYSIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FERROMAGNETIC MATERIAL;

ARTICLE; BOSON; CHEMICAL COMPOSITION; CHEMICAL INTERACTION; FERMION; FLOW KINETICS; FLOW MEASUREMENT; HARTREE FOCK EQUATION; HUBBARD MODEL; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; SCHWINGER DYSON EQUATION; TEMPERATURE DEPENDENCE;

EID: 14944372775     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevB.70.125111     Document Type: Article

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53. -3 the usual finite volume effects also formally lead to a vanishing order parameter. This is common to all other systems with spontaneous symmetry breaking. It is a well understood effect of no relevance to our issue.
54. Note that the result of the leading order Schwinger-Dyson equation is not consistent with the Mermin-Wagner theorem. Our more extended approximations based on the renormalization group equation will establish the missing consistency.
55. aã being observable.
56. There should be no confusion between the effective potential and the coupling in the Hubbard model which traditionally are both denoted by the letter U.
57. m/U=0.5. 43 Reference 4 uses a somewhat different formulation of the exact renormalization group equation.
58. k → ∞ the fluctuation contribution vanishes (up to a constant).
59. If needed, one may work in a finite volume such that the momentum sum is discrete.
60. Since we have regularized the propagators we may send Λ to very large values.
61. m from the location of the maximum in Fig. 12.
62. c. We note that the quantum critical behavior typically deviates from the universality class of the Heisenberg model if massless fermions are present (as in our case).
63. c has also been observed in a 1/d expansion (Ref. 33), with d the dimensionality of space. The precise connection with our result remains unclear, however, since the 1/d expansion at most partially captures the Goldstone boson physics.
64. c ≈ 2.9t in this case.
65. Of course, the third dimension may nevertheless, play a role for some realistic cuprates.