A Crossed Sliding Luttinger Liquid Phase

We study a system of crossed spin-gapped and gapless Luttinger liquids. We establish the existence of a stable non-Fermi liquid state with a finite-temperature,long-wavelength, isotropic electric conductivity that diverges as a power law in temperature $T$ as $T\to 0$. This two-dimensional system has many properties characteristic of a true isotropic Luttinger liquid, though at zero temperature it becomes anisotropic. This model can easily be extended to three dimensions.