Block renormalization study on the nonequilibrium chiral Ising model

Mina Kim, Su Chan Park, Jae Dong Noh

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4 Scopus citations


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 ξ∼t1/z and the domain-wall density ρ∼t-δ. The scaling exponents z and δ were found to vary continuously with the parameter u. To establish the anomalous power-law scaling firmly, we perform the block renormalization analysis proposed by Basu and Hinrichsen [U. Basu and H. Hinrichsen, J. Stat. Mech.: Theor. Exp. (2011) P110231742-546810.1088/1742-5468/2011/11/P11023]. The block renormalization method predicts, under the assumption of dynamic scale invariance, a scaling relation that can be used to estimate the scaling exponent numerically. We find the condition under which the scaling relation is justified. We then apply the method to our model and obtain the critical exponent zδ at several values of u. The numerical result is in perfect agreement with that of the previous study. This study serves as additional evidence for the claim that the nonequilibrium chiral Ising model displays power-law scaling behavior with continuously varying exponents.

Original languageEnglish
Article number012132
JournalPhysical Review E
Issue number1
StatePublished - 16 Jan 2015


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