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

The relaxation of the two-dimensional Ising model above Tc 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 Δ⁽ˡ⁾ of the linear relaxation time in a two-dimensional system. Also, the critical exponent, Δ⁽ⁿˡ⁾ of the nonlinear relaxation time is obtained: Δ^(nl)=1.932±0.018. These results support the Racz scaling law Δ⁽ˡ⁾=Δ^(nl)+β ({β} is the critical exponent of the order parameter).