Persistence properties of a phase-ordering system with competing dynamics

We investigate the persistence properties during phase ordering in the two-dimensional ($d=2$) Ising model evolving under competing nonconserved spin-flip and conserved spin-exchange dynamics by means of Monte Carlo simulations at zero temperature. We examine three distinct persistence probabilities: (i) the total persistence probability, defined as the probability that a lattice site has never experienced a change in the sign of the spin residing there; (ii) the spin-flip persistence probability, which exclusively measures the fraction of sites that have never undergone a spin-flip event; and (iii) the composite persistence probability, defined as the fraction of sites that have experienced neither a spin-flip nor a spin-exchange event. In the asymptotic regime, both the total and spin-flip persistence probabilities exhibit identical power-law decay, irrespective of the relative occurrence probability of the spin-flip move pᵣ. The corresponding persistence exponent θᵢ ≈ 0.225, is found to be consistent with the value reported for systems evolving purely under nonconserved dynamics. We further demonstrate that both persistence measures satisfy the scaling relation d-dfⁱ=θᵢ/αᵢ, where dfⁱ is the fractal dimension of the corresponding persistence lattice and αᵢ≈ 1/2 characterizes the asymptotic power-law growth of spatially correlated regions of non-persistent spins. In contrast, although the composite persistence probability also exhibits asymptotic power-law decay, both the corresponding persistence exponent θc and the fractal dimension dfᶜ of the persistence lattice show strong dependence on pᵣ. Combined with the presence of a universal growth exponent αc≈ 1/2, this leads to the breakdown of the scaling relation among the characteristic exponents for the composite persistence.