Fermions in two dimensions A total of N fermions of spin 12

Fermions in two dimensions. A total of N fermions (of spin 1/2 h and mass m) are restricted to motion in two dimensions on a plane of area A. There are no mutual interactions. For a temperature that satisfies the inequalities 0

Solution

We discuss interacting fermion models in two dimensions, and, in particular, such that can be solved exactly by bosonization. One solvable model of this kind was proposed by Mattis as an effective description of fermions on a square lattice. We review recent work on a specific relation between a variant of Mattis\' model and such a lattice fermion system, as well as the exact solution of this model. The background for this work includes well-established results for one-dimensional systems and the high-Tc problem. We also mention exactly solvable extensions of Mattis\' model.

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