New results for the dynamical critical behaviour of the two-dimensional Ising model

TL;DR

This paper reports large-scale simulations of the 2D Ising model revealing that the dynamical critical exponent z is approximately 2.167, challenging previous assumptions of z=2 with logarithmic corrections.

Contribution

The study provides new large-scale simulation data that refutes the old assumption of z=2, establishing a more accurate value of z≈2.167 for the 2D Ising model.

Findings

Large lattice simulations up to L=2,000,000.

Estimated dynamical critical exponent z≈2.167.

Logarithmic correction assumption for z is unlikely.

Abstract

Using the new supercomputer JUMP at the Research Center Juelich, we were able to simulate large lattices (up to L=2000000, meaning a new world record) for long times (up to T=6000 for L=150000). Using this data, we examined the dynamical critical exponent z. The old assumption of z=2 with logarithmic corrections seems very unlikely according to our data, leaving the asymptotic value of z~=2.167.