Remarks on coupled spin and charge fields in the Hubbard hamiltonian

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Abstract
This paper deals with the combined effect of spin and charge fluctuations on the thermodynamic properties of an itinerant electron paramagnet described by the Hubbard Hamiltonian. Firstly, we discuss the functional integral formulation of the partition function. We argue that a correct formulation must preserve the spin rotational invariance of the Hamiltonian. As a consequence, the Landau-Ginzburg-Wilson free energy functional contains both spin and charge fluctuation fields, with coupling terms of the form ρM2, ρ2 M2, etc... where p is a charge (scalar) field, and M is a vector spin field with 3 components. The relevant coupling between spin and charge fields is [FORMULA] where n(ε) is the density of states, εF is the Fermi level, and u is the intra-atomic Coulomb integral. It is pure imaginary. Next, we exploit the similarity between the free energy which we obtain and various other cases of coupled fields, such as metamagnets, or other phenomenological functionals. The role of constraints such as charge neutrality is discussed, with respect to critical properties, using the renormalization group method