Linear Resistivity from Spatially Random Interactions and the Uniqueness of Yukawa Coupling

Recent studies have shown that a spatially random Yukawa-type interaction between a Fermi surface and critical bosons can produce linear-in-temperature resistivity, the defining signature of strange metals. In this article, we systematically classify all scalar couplings of the form $(ψ^{\dagger}ψ)^nϕ^m$ in arbitrary dimensions to identify possible candidates for strange-metal behaviour within this disordered framework. We find that only the Yukawa-type interaction in $(2+1)$ dimensions yields linear resistivity. Combined with previous results showing that spatially random QED-type couplings also produce such linearity, we conclude that spatially random Yukawa and QED-type interactions exhaust the class of random couplings capable of producing linear resistivity.