Finite-temperature phase diagram of nonmagnetic impurities in high-temperature superconductors using a d = 3 t J model with quenched disorder

We study a quenched disordered $d=3\text{ }tJ$ Hamiltonian with static vacancies as a model of nonmagnetic impurities in high-${T}_{c}$ materials. Using a renormalization-group approach, we calculate the evolution of the finite-temperature phase diagram with impurity concentration $p$ and find several features with close experimental parallels: Away from half filling, we see the rapid destruction of a spin-singlet phase (analogous to the superconducting phase in cuprates) which is eliminated for $p\ensuremath{\gtrsim}0.05$; in the same region for these dilute impurity concentrations, we observe an enhancement of antiferromagnetism. The antiferromagnetic phase near half filling is robust against impurity addition and disappears only for $p\ensuremath{\gtrsim}0.40$.