We study the effect of $U=0$ impurities on the superconducting and thermodynamic properties of the attractive Hubbard model on a square lattice. Removal of the interaction on a critical fraction of $f_{\mathrm{crit}}\approx 0.30$ of the sites results in the destruction of off-diagonal long-range order in the ground state. This critical fraction is roughly independent of filling in the range $0.75<\rho <1.00$, although our data suggest that $f_{\mathrm{crit}}$ might be somewhat larger below half filling than at $\rho =1$. We also find that the two peak structure in the specific heat is present at $f$ both below and above the value which destroys long-range pairing order. It is expected that the high-$T$ peak associated with local pair formation should be robust, but apparently local pairing fluctuations are sufficient to generate a low-temperature peak.

• Received 8 July 2005

DOI:https://doi.org/10.1103/PhysRevB.72.144513