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We show that an interaction $U>0$ does lead to $\\lambda_2(U) > \\lambda_2(0)$ for not too large $U$ and test the validity of various proposed fit functions for $\\lambda_2(U)$. Finite-size scaling allows us to obtain infinite sample size estimates $\\xi_{2}(U)$ and we find that $ \\xi_{2}(U) \\sim \\xi_2(0)^{\\alpha(U)} $ with $\\alpha(U)$ varying between $\\alpha(0)\\approx 1$ and $\\alpha(1) \\approx 1.5$. 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