Short-Time Dynamics of an Ising Model with Competing Interactions

Abstract

In this work the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions is revisited. We obtain the dynamic critical exponents $z$ and $θ$ from short-time Monte Carlo simulations. The dynamic critical exponent $z$ was obtained from the time behavior of the ratio $F_2=< M^2>_{m_0=0}/< M>^2_{m_0=1}\sim t^{d/z}$, whereas the non-universal exponent $θ$ was estimated from the time correlation of the order parameter $<M(0)M(t)>\sim t^θ$, where $M(t)$ is the order parameter at instant $t$, $d$ is the dimension of the system and $<(...)>$ is the average of the quantity $(...)$ over different samples. We have also obtained the static critical exponents $β$ and $ν$ by investigating the time behavior of the magnetization.