Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India.
J Chem Phys. 2019 Feb 7;150(5):054702. doi: 10.1063/1.5052418.
Following quenches from random initial configurations to zero temperature, we study aging during evolution of the ferromagnetic (nonconserved) Ising model towards equilibrium, via Monte Carlo simulations of very large systems, in space dimensions d = 2 and 3. Results for the two-time autocorrelations exhibit scaling with respect to ℓ/ℓ, where ℓ and ℓ are the average domain sizes at t and t(⩽t), the observation and waiting times, respectively. The scaling functions are shown to be of power-law type for ℓ/ℓ → ∞. The exponents of these power-laws have been estimated via a novel application of the finite-size scaling method and discussed with reference to the available results from non-zero temperatures. While in d = 2 we do not observe any temperature dependence, in the case of d = 3 the outcome for quench to zero temperature appears different from the available results for high temperatures, which we explain via structural consideration. We also present results on the freezing phenomena that this model exhibits at zero temperature. Furthermore, from simulations of a very large system, thereby avoiding the freezing effect, it has been confirmed that the growth of average domain size in d = 3, that remained a puzzle in the literature, follows the Lifshitz-Allen-Cahn law in the asymptotic limit. We presented results for different acceptance probabilities for the spin flip trial moves. We observe slower growth for lower probability, even though the asymptotic exponent remains the same.
从随机初始构型到零温度的淬火后，我们通过对非常大的系统进行蒙特卡罗模拟，研究了铁磁（非守恒）伊辛模型在向平衡态演化过程中的老化现象，空间维度为 d = 2 和 3。两个时间自相关的结果表现出相对于 ℓ/ℓ 的标度，其中 ℓ 和 ℓ 分别是 t 和 t（⩽t）时的平均畴大小，观察和等待时间。观察到这些标度律的标度函数具有幂律类型，对于 ℓ/ℓ → ∞。通过有限大小标度方法的新应用，估计了这些幂律的指数，并参考了非零温度下可用的结果进行了讨论。虽然在 d = 2 中我们没有观察到任何温度依赖性，但在零温度淬火的情况下，结果与高温下可用的结果不同，我们通过结构考虑对此进行了解释。我们还介绍了该模型在零温度下表现出的冻结现象的结果。此外，通过对非常大的系统进行模拟，从而避免了冻结效应，已经证实，在 d = 3 中，平均畴大小的增长在渐近极限下遵循 Lifshitz-Allen-Cahn 定律，这在文献中一直是个谜。我们呈现了不同自旋翻转试验移动接受概率的结果。我们观察到较低概率的增长较慢，尽管渐近指数保持不变。
