Finite- Size Scaling of Correlation Function

We propose the finite-size scaling of correlation function in a finite system near its critical point. At a distance $\mathbf{r}$ in the finite system with size $L$, the correlation function can be written as the product of $|{\bf r}|^{-(d-2+\eta)}$anditsfinite-sizescalingfunctionofvariables${\bf r}/L$and$tL^{1/\nu}$,where$t=(T-T_c)/T_c$. The directional dependence of correlation function is nonnegligible only when $\mathrm{\mid }\mathbf{r}\mathrm{\mid }$ 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 $\eta$.