Block renormalization study on the nonequilibrium chiral Ising model

TL;DR

This paper investigates the nonequilibrium chiral Ising model's ordering dynamics, revealing continuous variation of scaling exponents and universal block spin indices through numerical simulations and renormalization analysis.

Contribution

It applies block spin renormalization to confirm the continuous variation of scaling exponents in the chiral Ising model, providing new evidence for anomalous power-law scaling.

Findings

Scaling exponents vary continuously with parameter u.

Block spin indices are universal and depend on u.

Numerical results align with previous scaling studies.

Abstract

We present a numerical study on the ordering dynamics of a one-dimensional nonequilibrium Ising spin system with chirality. This system is characterized by a direction-dependent spin update rule. Pairs of $+-$ spins can flip to $++$ or $--$ with probability $(1-u)$ or to $-+$ with probability $u$ while $-+$ pairs are frozen. The system was found to evolve into the ferromagnetic ordered state at any $u<1$ exhibiting the power-law scaling of the characteristic length scale $\xi\sim t^{1/z}$ and the domain wall density $\rho\sim t^{-\delta}$. The scaling exponents $z$ and $\delta$ were found to vary continuously with the parameter $u$. In order to establish the anomalous power-law scaling firmly, we perform the block spin renormalization analysis proposed by Basu and Hinrichsen [U. Basu and H. Hinrichsen, J. Stat. Mech. (2011) P11023]. Domain walls of $b$ sites are coarse-grained into a block spin $\sigma^b$, and the relative frequencies of two-block patterns $\sigma^b_1 \sigma^b_2$ are measured in the $b\to\infty$ and $t\to\infty$ limit. These indices are expected to be universal. By performing extensive Monte Carlo simulations, we find that the indices also vary continuously with $u$ and that their values are consistent with the scaling exponents found in the previous study. This study serves as another evidence for the claim that the nonequilibrium chiral Ising model displays the power-law scaling behavior with continuously varying exponents.