Short-time critical dynamics of the Ising model studied within the N-fold algorithm

The short-time behaviour of the critical two-dimensional Ising model is studied for the Bortz–Kalos–Lebowitz N-fold way algorithm (BKL algorithm). For square lattices of linear sizes L=110, 128, 140, 170, and 200, we calculate the short-time critical behaviour for the BKL algorithm and also for the heat-bath algorithm. Comparison of these results shows that, although power-law scaling form emerges from the early times of the dynamics, there are noticeable differences, which do not produce negligible effects on the estimates of critical exponents. The observed universality of short-time critical behaviour supplements our fundamental knowledge of critical phenomena. However, short-time dynamics seem to be related only approximately with equilibrium critical properties. Therefore, any attempt to estimate equilibrium critical exponents from the short-time regime would be superfluous, except for the purpose of comparison, because these exponents have been determined very precisely by different methods.