Explicit dynamic finite-size scaling in the time-dependent correlation functions for the two-dimensional classical XY model is explored. The dynamic scaling method, proposed by us previously, is utilized for finding the time scaling variables of the model. It shows nontrivial dynamic finite-size scaling behavior near and below TKT for the total spin correlation function. Since the model is critical for all temperatures below TKT, the time scaling exponent is markedly different from that of the three-dimensional classical XY model at short times. There also appears to be another dynamic scaling region with a different time scaling exponent at T⩽TKT for a fairly wide intermediate time interval.Explicit dynamic finite-size scaling in the time-dependent correlation functions for the two-dimensional classical XY model is explored. The dynamic scaling method, proposed by us previously, is utilized for finding the time scaling variables of the model. It shows nontrivial dynamic finite-size scaling behavior near and below TKT for the total spin correlation function. Since the model is critical for all temperatures below TKT, the time scaling exponent is markedly different from that of the three-dimensional classical XY model at short times. There also appears to be another dynamic scaling region with a different time scaling exponent at T⩽TKT for a fairly wide intermediate time interval.

Journal of Applied PhysicsApr 15, 19971 citation

Dynamic finite-size effect in the three-dimensional classical XY model

Suhk Kun Oh, Chang No Yoon, Jean Soo Chung

Explicit dynamic finite-size scaling in the time-dependent correlation functions for the three-dimensional classical $\mathrm{XY}$ model is explored. The dynamic scaling method, proposed by us previously, is utilized for finding the time-scaling variables of the model. Time-dependent correlation functions of the model for different numbers of spins could be collapsed into universal curves. Compared to infinite-range spin models, the width of the scaling region is found to be much narrower.Explicit dynamic finite-size scaling in the time-dependent correlation functions for the three-dimensional classical $\mathrm{XY}$ model is explored. The dynamic scaling method, proposed by us previously, is utilized for finding the time-scaling variables of the model. Time-dependent correlation functions of the model for different numbers of spins could be collapsed into universal curves. Compared to infinite-range spin models, the width of the scaling region is found to be much narrower.

Physical review. B, Condensed matterDec 1, 19973 citations

Finite-size scaling and the renormalization group

Joseph Rudnick, Hong Min Guo, David Jasnow

Journal of Statistical PhysicsNov 1, 1985157 citations

Finite-Size Scaling and the Renormalization Group

Joseph Rudnick, Hong Mei Guo, David Jasnow

Current physics sources and commentsJan 1, 19882 citations

Finite- Size Scaling of Correlation Function

Xin Zhang, Gaoke Hu, Yongwen Zhang +2 more

We propose the finite-size scaling of correlation function in a finite system near its critical point. At a distance ${\bf r}$ in the finite system with size $L$ , the correlation function can be written as the product of $|{\bf r}|^{-(d-2+η)}$ and its finite-size scaling function of variables ${\bf r}/L$ and $tL^{1/ν}$ , where $t=(T-T_c)/T_c$ . The directional dependence of correlation function is nonnegligible only when $|{\bf r}|$ becomes compariable with $L$ . This finite-size scaling of correlation function has been confirmed by correlation functions of the Ising model and the bond percolation in two-diemnional lattices, which are calculated by Monte Carlo simulation. We can use the finite-size scaling of correlation function to determine the critical point and the critical exponent $η$ .We propose the finite-size scaling of correlation function in a finite system near its critical point. At a distance ${\bf r}$ in the finite system with size $L$, the correlation function can be written as the product of $|{\bf r}|^{-(d-2+η)}$ and its finite-size scaling function of variables ${\bf r}/L$ and $tL^{1/ν}$, where $t=(T-T_c)/T_c$. The directional dependence of correlation function is nonnegligible only when $|{\bf r}|$ becomes compariable with $L$. This finite-size scaling of correlation function has been confirmed by correlation functions of the Ising model and the bond percolation in two-diemnional lattices, which are calculated by Monte Carlo simulation. We can use the finite-size scaling of correlation function to determine the critical point and the critical exponent $η$.

arXiv:1805.08607May 22, 20181 citation

Explicit dynamic finite-size scaling in the time-dependent correlation functions for the three-dimensional classical

\mathrm{XY}

model is explored. The dynamic scaling method, proposed by us previously, is utilized for finding the time-scaling variables of the model. Time-dependent correlation functions of the model for different numbers of spins could be collapsed into universal curves. Compared to infinite-range spin models, the width of the scaling region is found to be much narrower.

We propose the finite-size scaling of correlation function in a finite system near its critical point. At a distance

{\bf r}

in the finite system with size

L

, the correlation function can be written as the product of

|{\bf r}|^{-(d-2+η)}

and its finite-size scaling function of variables

{\bf r}/L

and

tL^{1/ν}

, where

t=(T-T_c)/T_c

. The directional dependence of correlation function is nonnegligible only when

|{\bf r}|

becomes compariable with

L

. This finite-size scaling of correlation function has been confirmed by correlation functions of the Ising model and the bond percolation in two-diemnional lattices, which are calculated by Monte Carlo simulation. We can use the finite-size scaling of correlation function to determine the critical point and the critical exponent

η