Block renormalization study on the nonequilibrium chiral Ising model

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 ${\sigma }_1^b{\sigma }_2^b$ 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.

arXiv comment9 pages, 6 figures

References in corpus (20)

• Revisiting the flocking transition using active spins
• Strong disorder fixed point in absorbing state phase transitions
• Growth Laws for Phase Ordering
• Distribution of domain sizes in the zero temperature Glauber dynamics of the 1 D Potts model
• Domain Statistics in Coarsening Systems
• Nonequilibrium phase transition on a randomly diluted lattice
• Propagation and Extinction in Branching Annihilating Random Walks
• Inter-Particle Distribution Functions for One-Species Diffusion-Limited Annihilation, A+A->0
• Correlation Functions for Diffusion-Limited Annihilation, A + A -> 0
• Nonequilibrium Kinetic Ising Models: Phase Transition and Universality Classes in One Dimension
• Solution of classical stochastic one dimensional many-body systems
• Branching-annihilating random walks in one dimension: Some exact results
• Three-Species Diffusion-Limited Reaction with Continuous Density-Decay Exponents
• Two-point correlation functions of the diffusion-limited annihilation in one dimension
• Passage-time moments and hybrid zones for the exclusion-voter model
• Critical dynamics of nonconserved $N$-vector model with anisotropic nonequilibrium perturbations
• One-dimensional spin-anisotropic kinetic Ising model subject to quenched disorder
• Identifying universality classes of absorbing phase transitions by block renormalization
• Nonuniversal exponents in sandpiles with stochastic particle number transfer
• Coarsening Dynamics of Nonequilibrium Chiral Ising Models

Cited by in corpus (3)

• Flocking with discrete symmetry: the 2d Active Ising Model
• One-dimensional annihilating random walk with long-range interaction
• How to experimentally probe universal features of absorbing phase transitions using steady state