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In this paper, we use the Replica-Exchange Wang–Landau (REWL) technique to study the behavior of the two-point correlation function of the site diluted classical anisotropic Heisenberg (AH) model in two dimensions. The model has a topological Berezinskii–Kosterlitz–Thouless (BKT) transition for any dilution down to the percolation threshold, ρ th ≈ 0. 5 9 2 7 5. Contrary to earlier results that predict the exponent of the correlation function, η , to decay linearly to zero as a function of temperature, we found that it decreases with temperature to a finite value η 0 at T → 0 for any dilution ρ th ≤ ρ ≤ 1. [ABSTRACT FROM AUTHOR]