Fluctuating orders and quenched randomness in the cuprates

We study a quasi-2D classical Landau-Ginzburg-Wilson effective field theory in the presence of quenched disorder in which incommensurate charge-density wave and superconducting orders are intertwined. The disorder precludes long-range charge-density wave order, but not superconducting or nematic order. We select three representative sets of input parameters and compute the corresponding charge-density wave structure factors using both large-\(N\) techniques and classical Monte Carlo simulations. Where nematicity and superconductivity coexist at low temperature, the peak height of the charge-density wave structure factor decreases monotonically as a function of increasing temperature, unlike what is seen in X-ray experiments on YBa\(_2\)Cu\(_3\)O\(_{6+x}\). Conversely, where the thermal evolution of the charge-density wave structure factor qualitatively agrees with experiments, the nematic correlation length, computed to one-loop order, is shorter than the charge-density wave correlation length.