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Universality Class of the Antiferromagnetic Transition in the Two Dimensional Hubbard Model

The antiferromagnetic transition of the two dimensional Hubbard model is analyzed by comparing the available exact, numerical and mean field results. It is argued that all data is compatible with the opening of a mean field gap in a Fermi liquid of spin polarons, the so called Slater type of transition. In particular, this hypothesis explains the unusual dispersion relation of the quasiparticle bands near the transition. PACS. 71.10.Fd Lattice fermion models (Hubbard model, etc.) – 71.30.+h Metal-insulator transitions and other electronic transitions The nature of the insulating phase of the Hubbard model has attracted a great deal of attention. A clarification of the universality class of the transition will greatly help in understanding the nature of the “metallic ”, gapless phase away from half doping. A detailed discussion of the issue can be found in [1]. Opposing viewpoints on the problem are presented in [2,3]. An appealing approach is the scaling analysis discussed in [1]. It is assumed that physical quantities can be expressed in terms of a single energy scale, ∆, which vanishes at the transition. A wealth of numerical results suggest that such scaling does exist. The data implies that typical length scales, ξ, scale