On page 526 of your paper Self-driven lattice-model Monte Carlo simulations of alloy thermodynamic properties and phase diagrams' (Modelling Simul. Mater. Sci. Eng. 10 (2002) 521-538) , you calculate the parameter row’ by searching parameter l*' where Vl*/V0=1/2’. Could you explain to me why you choose 1/2 ? Did you select this value based on an error analysis, or was there another reason?
The choice of 1/2 is driven by minimizing noise: if the ratio is too close to 0, the noise is large relative to the signal, while if the ratio is close to 1, we magnify noise as we determine the correlation length from that information. 1/2 seemed like the best compromise, althogh I have not worked out the formal mathematical argument.