Figure 1

Dynamic relaxation from a semiordered state is simulated for the 2D Ising model at the critical temperature. The spin configuration of the domain interface is shown in a spatial window $\left[-40,40\right]$ at the time $t=0,10,100,1000$ (from left to right). Black points denote $S_i=-1$ and white points denote $S_i=1$. The lattice size $L=256$ is used in the Monte Carlo simulations.Reuse & Permissions

Figure 2

The magnetization of the 2D Ising model starting from the semiordered state is plotted with solid lines on a double-log scale. Dashed lines show the power-law fits. According to Eq. (8), data collapse for different $x$ is demonstrated at a fixed $x^{\prime }=1.5$. Solid circles, solid squares, solid triangles, pluses, open circles, open squares, and open triangles correspond to $x=0.5$, 1.5, 3.5, 7.5, 15.5, 31.5, and 63.5, respectively. From Ref. [56], this figure is reproduced by permission of Europhys. Lett.Reuse & Permissions

Figure 3

The scaling functions $\tilde{M}\left(s\right)$ with $s=t^{1/z}/x$ is plotted on a double-log scale, for the 2D Ising model with the free surface, disordered surface, and domain interface (from above). Data collapse for different $x$ is observed. Dashed lines show the power-law fits. From Ref. [56], this figure is reproduced by permission of Europhys. Lett.Reuse & Permissions

Figure 4

The magnetization of the 2D Ising with a free surface and starting from an ordered state, is plotted with solid lines on a double-log scale. Dashed lines show the power-law fits. According to Eq. (8), data collapse for different $x$ is demonstrated at a fixed $x^{\prime }=2$. Solid circles, solid triangles, pluses, open circles, open squares, and open triangles correspond to $x=1$, 4, 8, 16, 32, and 64, respectively.Reuse & Permissions

Figure 5

The scaling function $\tilde{M}\left(s\right)$ with $s=t^{1/z}/x$ is plotted on a double-log scale, for the 3D Ising model with the free surface, disordered surface, and domain interface (from above). Data collapse for different $x$ is observed. Dashed lines show the power-law fits. No logarithmic correction is detected for the disordered surface. In the inset, the magnetization at $x=1.0$ for the disordered surface and free surface are shown.Reuse & Permissions

Figure 6

The Binder cumulant of the 2D Ising model with the domain interface is plotted with solid lines on a double-log scale. Dashed lines show the power-law fits. According to Eq. (9), data collapse for different $x$ is demonstrated at a fixed $x^{\prime }=1.5$. Solid squares, solid triangles, pluses, open circles, open squares, and open triangles correspond to $x=0.5$, 3.5, 7.5, 15.5, 31.5, and 63.5, respectively.Reuse & Permissions

Figure 7

The Binder cumulant of the 3D Ising model with the domain interface is plotted with solid lines on a double-log scale. Dashed lines show the power-law fits. According to Eq. (9), data collapse for different $x$ is demonstrated at a fixed $x^{\prime }=1.5$. Solid circles, solid triangles, pluses, open circles, open squares, and open triangles correspond to $x=0.5,3.5,7.5,15.5,31.5,63.5$, respectively.Reuse & Permissions

Figure 8

The Binder cumulant at $x=0.5$ for the Ising model with the domain interface is plotted with solid lines on a double-log scale. The lower three solid lines are for the 2D Ising model with the lattice size $L=128$, 256, and 512. The $x$ and $y$ axes are on the bottom and right sides. According to Eq. (9), the curves collapse to the curve at $L^{\prime }=256$. Circles and triangles correspond to $L=512$ and 128, respectively. The upper three solid lines are for the 3D Ising model with $L=32$, 64, and 128. The $x$ and $y$ axes are on the top and left sides. Data collapse is observed. Circles and triangles correspond to $L=128$ and 32, respectively.Reuse & Permissions

Figure 9

The scaling function $\tilde{U}\left(s\right)$ with $s=t^{1/z}/x$ is plotted on a double-log scale, for the 2D Ising model with the domain interface and free surface. Data collapse for different $x$ is observed. The dashed line shows the power law fit, and the solid line indicates the logarithmic fit.Reuse & Permissions

Figure 10

The height function $h\left(t\right)$ of the 2D Ising model is plotted on a double-log scale. The three upper solid lines are for the domain interface, free surface, and bulk (from below). The lower solid lines are the pure height function $Dh\left(t,L\right)$ of the free surface and domain interface (from below). Dashed lines show the power-law fits, and stars are from a double power-law fit.Reuse & Permissions

Figure 11

The roughness function ${\omega }^2\left(t\right)$ of the 2D Ising model is plotted on a double-log scale. The three upper solid lines are for the domain interface, free surface, and bulk (from above). The lower solid lines are the pure roughness function $D{\omega }^2\left(t,L\right)$ for the domain interface and free surface (from above). Dashed lines show the power-law fits, and stars are from a double power-law fit.Reuse & Permissions

Figure 12

The pure roughness function $D{\omega }^2\left(t,L\right)$ of the domain interface is plotted for the 2D Ising model with solid lines on a double-log scale, for $L=512$, 256, 128, and 64 (from below). According to Eq. (19), data collapse is observed at the curve of $L^{\prime }=256$. Solid circles, solid squares, and solid triangles correspond to $L=512$, 128, and 64, respectively.Reuse & Permissions