FIG. 6.

Finite-size scaling. We define the h-dependent operator ${\widehat{A}}_h$ through Eq. (C1), which allows us to connect the physical value of h = 0.275 798 for the heptagonal lattice to a formal h → 0 limit. For the radially symmetric test function f(r) = cos[πd(r, 0)] we show here ${\widehat{A}}_{h}f$ (empty black circles), the cubic approximation ${\widehat{A}}_h^{\left(3\right)}f$ from Eq. (C3) (filled blue squares), and the quadratic approximation ${\widehat{A}}_h^{\left(2\right)}=3f+\frac{3}{4}{h}^2{\Delta }_{g}f$ (gray solid line). We subtract 3f for better visibility of the deviations. The three figures correspond to decreasing values of h, with the individual values given in the plot labels. As h → 0, the quadratic approximation quantitatively reproduces the full expression.