Correlations and Néel Order of Randomly Diluted Quantum Spin Ladders

We present a Monte Carlo study of the correlation length ξ of randomly diluted antiferromagnetic spin- 1/2 two-chain Heisenberg ladders with weak and intermediate interchain couplings, J_⊥/J≤1. We are able to access the experimentally relevant low-temperature regime, T/J≈1/500, and find (i) that the form ξ(z,T)0ex0ex=0ex0exA(z)+B(z)T^-ν, with ν0ex0ex=0ex0ex0.40(5), describes our data at low and moderate dilution z and up to rather high temperatures, (ii) evidence for scaling of ξJ_⊥/J in the variable zJ/J_⊥ at weak J_⊥/J, (iii) an enhancement of correlations that is strongest for a fraction z*≈J_⊥/(8J) of dilutants, and (iv) that the N\'eel temperature of Sr(Cu_1-zZnz)₂O₃ corresponds well to a curve of constant correlation length ξ0ex0ex=0ex0ex18(2) of the single diluted ladder with J_⊥/J1/2.