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We calculate the resistivity associated with an Ising-nematic quantumcritical point in the presence of disorder and acoustic phonons in the latticemodel. We use the memory-matrix transport theory, which has a crucial advantagecompared to other methods of not relying on the existence of well-definedquasiparticles in the low-energy effective theory. As a result, we obtain thatby including an inevitable interaction between the nematic fluctuations and theelastic degrees of freedom of the lattice (parametrized by the nemato-elasticcoupling $\kappa_{\text{latt}}$), the resistivity $\rho(T)$ of the system as afunction of temperature obeys a universal scaling form described by$\rho(T)\sim T\ln (1/T)$ at high temperatures, reminiscent of the paradigmaticstrange metal regime observed in many strongly correlated compounds. For awindow of temperatures comparable with$\kappa^{3/2}_{\text{latt}}\varepsilon_F$ (where $\varepsilon_F$ is the Fermienergy of the microscopic model), the system displays another regime in whichthe resistivity is consistent with a description in terms of $\rho(T)\simT^{\alpha}$, where the effective exponent roughly satisfies the inequality$1\lesssim\alpha\lesssim 2$. However, in the low-temperature limit (i.e.,$T\ll\kappa^{3/2}_{\text{latt}}\varepsilon_F$), the properties of the quantumcritical state change in an important way depending on the types of disorderpresent in the system: It can either recover a conventional Fermi liquiddescribed by $\rho(T)\sim T^2$ or it could exhibit yet another non-Fermi liquidregime characterized by the scaling form $\rho(T)-\rho_0\sim T^2\ln T$. Ourresults emphasize the key role played by both phonon and disorder effects inthe scenario of nematic quantum criticality and might be fundamental foraddressing recent transport experiments in some iron-based superconductors.

DC resistivity near a nematic quantum critical point: Effects of weak disorder and acoustic phonons