Non-Fermi-liquid theory for disordered metals near two dimensions

We consider the Finkelstein action describing a system of spin-polarized or spinless electrons in 2+2ε dimensions, in the presence of disorder as well as the Coulomb interactions. We extend the renormalization-group analysis of our previous work and evaluate the metal-insulator transition of the electron gas to second order in an ε expansion. We obtain the complete scaling behavior of physical observables like the conductivity and the specific heat with varying frequency, temperature, and/or electron density. We extend the results for the interacting electron gas in 2+2ε dimensions to include the quantum critical behavior of the plateau transitions in the quantum Hall regime. Although these transitions have a very different microscopic origin and are controlled by a topological term in the action (θ term), the quantum critical behavior is in many ways the same in both cases. We show that the two independent critical exponents of the quantum Hall plateau transitions, previously denoted as ν and p, control not only the scaling behavior of the conductances σₓₓ and σxy at finite temperatures T, but also the non-Fermi-liquid behavior of the specific heat (cᵥ∝Tᵖ). To extract the numerical values of ν and p it is necessary to extend the experiments on transport to include the specific heat of the electron gas.