Abstract
A one-dimensional nonequilibrium kinetic Ising model possessing two symmetricabsorbing states exhibits simultaneous occurrence of two distinct phase transitions,namely the order–disorder transition and the active–absorbing transition. Westudy the coarsening (both critical and subcritical) process evolving towards thenonequilibrium steady state of this model via the spatial correlations of the orderparameters and their dynamic scaling features. For critical coarsening, the lengthscales associated with the two transitions exhibit the same superdiffusive growthbehavior. Critical dynamic scaling behaviors satisfied by the order parametercorrelations provide a general relationship between the defect relaxation and thegrowing length scale. Some of the standard scaling relations between the staticcritical exponents for the order–disorder transition are found to be modified for theabsorbing transition. For subcritical coarsening, the defect correlation exhibitsnon-monotonic spatial structure due to the interplay between branching and annihilationprocesses of defects. This structure reveals that, in addition to the usual diffusivelygrowing length scale, there exists a new length scale that grows subdiffusively intime.
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