Erratum: Critical properties of a two-dimensional Ising magnet with quasiperiodic interactions [Phys. Rev. E 93, 042111 (2016)]

Figure 3

Binder cumulant $g_L$ vs temperature $T$ for different lattice sizes $L$. The values of $L$ obey the Fibonacci sequence. We estimated the critical temperature $T_c\approx 1.268$ by averaging the numerical values of the temperatures where the curves intersect each other. We have, for this model, a phase transition from a paramagnetic phase to a spin-glass phase by decreasing the temperature.

Figure 4

The EA order parameter $q_{EA}$ as a function of temperature $T$ for different lattice sizes $L$. The values of $L$ obey the Fibonacci sequence. The curves suggest a second order phase transition.

Figure 5

Critical behavior of $q_{EA}$ at $T=T_c$ as a function of lattice size $L$ obtained from Eq.(6) of our original article. Alongside the $q_{EA}$ points we show the error bars on the same scale. The curve slope gives the exponent ratio $\beta /\nu =0.24\left(1\right)$. The exponent ratio differs from the pure model and this change of the universality class is induced by the quasiperiodic ordering.

Figure 7

The susceptibility $\chi$ as a function of temperature $T$ for different lattice sizes $L$. The values of $L$ obey the Fibonacci sequence. The susceptibility diverges at $T_c$ in the large lattice size limit suggesting a second order phase transition.

Figure 8

Critical behavior of $\chi$ at $T=T_c$ as a function of lattice size $L$ obtained from Eq.(7) of our original article. Alongside the $\chi$ points we show the error bars on the same scale. The curve slope gives the exponent ratio $\gamma /\nu =1.50\left(1\right)$, differing from the pure Ising 2D case.

Figure 9

Critical behavior of susceptibility maximum temperatures $T_{\chi }$ as a function of lattice size $L$ obtained from Eq.(10) of our original article. The curve slope gives the exponent $1/\nu =0.89\left(3\right)$, differing from the pure Ising 2D case.

Figure 10

Specific heat $c$ as a function of temperature $T$ for different lattice sizes $L$. The values of $L$ obey the Fibonacci sequence. When increasing the lattice size, we observe a crescent maximum, suggesting a logarithm divergence or a negative exponent divergence at the critical temperature $T_c\approx 1.268$.

Figure 11

Data collapse of specific heat $c$ for different lattice sizes $L$. The best data collapse gives us the estimate for $\alpha /\nu \approx -0.24$.

Figure 12

Data collapse of EA order parameter $q_{EA}$ and susceptibility $\chi$. The thermodynamic parameters as functions of lattice sizes collapse for $\beta /\nu =0.24\left(1\right),\gamma /\nu =1.50\left(1\right)$, and $1/\nu =0.89\left(3\right)$ next to the critical temperature according to the scale forms given in Eqs. (6) and (7) of our original article differing from the pure Ising 2D case.