Abstract
We consider the correction ee due to electron-electron interaction to the conductivity of a weakly disordered metal Altshuler-Aronov correction. The correction is related to the spectral determinant of the Laplace operator. The case of a large square metallic network is considered. The variation of eeLT as a function of the thermal length LT is found very similar to the variation of the weak localization WLL as a function of the phase coherence length. Our result for ee interpolates between the known one-dimensional 1D and two-dimensional 2D results, but the interaction parameter entering the expression of ee keeps a 1D behavior. Quite surprisingly, the result is very close to the 2D logarithmic behavior already for LTa/2, where a is the lattice parameter.
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