Finite-Temperature Phase Diagram of the $d=3$ $tJ$ Model with Quenched Disorder

We study a quenched disordered $d=3$ $tJ$ Hamiltonian with static vacancies as a model of nonmagnetic impurities in high-$T_c$ materials.[1,2] Using a position-space 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 liquid phase (analogous to the superconducting phase in cuprates) which is eliminated for $p \ge 0.05$; 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 $p \ge 0.40$. \newline \noindent [1] M. Hinczewski and A.N. Berker, Eur. Phys. J. B {\bf 51}, 461 (2006). \newline \noindent [2] M. Hinczewski and A.N. Berker, arXiv:cond-mat/0607171v1 [cond-mat.str-el].