Comment on “Elastic constants from microscopic strain fluctuations”

Sengupta et al. [Phys. Rev. E 61, 1072 (2000)] presented an elegant and simple finite-size scaling method for the calculation of elastic constants and their corresponding correlation lengths, which is suitable for many finite discrete systems considered through simulations or experiments. We take into account a mathematical finite-size effect that was neglected by the authors in order to propose a more accurate method. Consequences on the authors’ results are also discussed.

Figure 1

Theoretical curves for $x{f}_L\left(\xi ,\chi ,x\right)$ as a function of $x=L_b/L$ for different $L$. Symbols: using ${\psi }_{\text{Sengupta}}$ (Eq. (12)) with $\chi =1$ and $\xi =1$. Full lines: fits with the proposed $\psi$ (Eq. (11)).

Figure 2

Values for $\chi$ and $\xi$ found with our function $\psi$, to be compared with the values $\chi =1$ and $\xi =1$ that would be found with function ${\psi }_{\text{Sengupta}}$, for different system sizes $L$.