Nonequilibrium critical relaxation at a first-order phase transition point

We study numerically the nonequilibrium dynamical behavior of an Ising model with mixed two-spin and four-spin interactions after a sudden quench from the high-temperature phase to the first-order phase transition point. The autocorrelation function is shown to approach its limiting value, given by the magnetization in the ordered phase at the transition point, mc, through a stretched exponential decay. On the other hand relaxation of the magnetization starting with an uncorrelated initial state with magnetization, mi, approaches either mc, for $m_{i} > 0.5$, or zero, for $m_{i} < 0.5$. For small mi and for mi slightly larger than 0.5 the relaxation of the magnetization shows an asymptotic power law time dependence, thus from a nonequilibrium point of view the transition is continuous