The scaling behavior can be further tested by plotting R X L,k (θ) vs (θ − θ p,k ) L 1/ν , P L β/ν vs |θ − θ p,k |L 1/ν and χL −γ/ν vs (θ − θ p,k ) L 1/ν and looking for data collapsing [1]. Figs. 1 and 2 show the excellent collapse of curves of R A L,k (a), P (b), χ (c) and the cumulant U L (d), for two typical cases (k = 8 and k = 32) and different lattice sizes, as indicated. The plots were made using the value of θ p,k=8 = 0.4118 and θ p,k=32 = 0.4303 calculated above and the exact values of the critical exponents of the ordinary percolation ν = 4/3, β = 5/36 and γ = 43/18. This leads to independent controls and consistency checks of the values of all the critical exponents.
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