Vectorized Monte Carlo simulation of large Ising models near the critical point

The relaxation of the two-dimensional Ising model above $T_c$ for lattices with size up to 10 240×10 240 is studied by the Monte Carlo simulation in vectorized super-spin-coding on the HITAC S-810/20 supercomputer. The present estimation of the dynamic critical exponent z gives z=2.076±0.005, which is equal to the critical exponent ${\Delta }^{\left(l\right)}$ of the linear relaxation time in a two-dimensional system. Also, the critical exponent, ${\Delta }^{\mathrm{}\left(\mathrm{nl}\right)\mathrm{}}$ of the nonlinear relaxation time is obtained: ${\Delta }^{\mathrm{}\left(\mathrm{nl}\right)\mathrm{}=1.932\mathrm{}\pm 0.018}$. These results support the Racz scaling law ${\Delta }^{\left(l\right)}$=${\Delta }^{\mathrm{}\left(\mathrm{nl}\right)\mathrm{}+\mathrm{\beta }}$ (β is the critical exponent of the order parameter).