Short-Time Dynamics of an Ising Model with Competing Interactions

TL;DR

This paper investigates the short-time dynamics of a two-dimensional Ising model with competing interactions, estimating dynamic and static critical exponents through Monte Carlo simulations.

Contribution

It provides new estimates of dynamic critical exponents $z$ and $ heta$, and static exponents $eta$ and $ u$ for the Ising model with next-nearest interactions.

Findings

Estimated dynamic critical exponent $z$ from Monte Carlo simulations.

Estimated non-universal exponent $ heta$ from time correlation.

Determined static critical exponents $eta$ and $ u$ from magnetization behavior.

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 $\theta$ 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 $\theta$ was estimated from the time correlation of the order parameter $<M(0)M(t)>\sim t^{\theta}$, 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 $\beta$ and $\nu$ by investigating the time behavior of the magnetization.