Large-scale Simulation of the Two-dimensional Kinetic Ising Model

TL;DR

This paper reports large-scale Monte Carlo simulations of the 2D kinetic Ising model to accurately determine the dynamical critical exponent, using extensive lattices and two different dynamics methods.

Contribution

It provides a highly precise estimate of the dynamical critical exponent for the 2D kinetic Ising model through large-scale simulations and analysis of relaxation dynamics.

Findings

Dynamical critical exponent z = 2.16 ± 0.005

Consistent results with Glauber and Metropolis dynamics

Large lattice size improves accuracy of critical exponent measurement

Abstract

We present Monte Carlo simulation results for the dynamical critical exponent $z$ of the two-dimensional kinetic Ising model using a lattice of size $10^6 \times 10^6$ spins. We used Glauber as well as Metropolis dynamics. The $z$-value of $2.16\pm 0.005$ was calculated from the magnetization and energy relaxation from an ordered state towards the equilibrium state at $T_c$.