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) = A(z) + B(z)T^-ν, with ν = 0.40(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 Néel temperature of Sr(Cu_1-zZn_z)₂O₃ corresponds well to a curve of constant correlation length ξ = 18(2) of the single diluted ladder with J_⊥/J≤1/2.