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High precision Monte Carlo simulations are used to study domain growth in a compressible two-dimensional spin-exchange Ising model with continuous particle positions and zero total magnetization. For mismatched systems, we measure significant deviations from the theoretically expected late-time domain growth, R(t) = A + Btⁿ with n = 1/3. For a compressible model with no mismatch, we measure only a slight deviation from n = 1/3. Our results indicate that our current understanding of domain growth is incomplete.

The phase-separating system coupled with a simple reversible reaction A ⇌ B in a binary immiscible mixture due to critical quench is investigated with Lowe-Andersen temperature controlling method in two dimensions. The system viscosity strongly influences the asymptotic relationship between the excess energy (characterizing the domain growth) and the reaction rate. The competition between different dynamic factors results in the steady states with characteristic domain sizes. For low viscosities, the domain growth exponent approximates to 0.4 in the cases of low reaction rates and to 0.25 in the cases of high reaction rates, which shows the suppressing effects of high reversible reaction rates on the phase separation. However, in the cases of high viscosities, we find a 0.25 scaling with low reaction rates but a 0.5 scaling with high reaction rates. In these cases, high viscosities prevent mass transport in the binary mixture, consequently result in much smaller steady state domain sizes. Therefore the domain sizes with high viscosities and low reaction rates are very similar to those with low viscosities and high reaction rates, and the dependence of domain sizes on the reaction rates are similar. For the high-viscosity systems with high reaction rates, the domain sizes are predominantly controlled by the reaction rates, therefore we can observe stronger dependence of domain size on the reaction rate.

The temperature dependence of the dynamics of the fraction F(t) of persistent spins in the triangular Q-state Potts model is investigated by large scale Monte Carlo simulations. After extending Derrida's approach of measuring the fraction of spins that remain in one phase to allQ low-temperature phases, it is shown that the exponent θ of algebraic decay of F(t) is independent of temperature.