论文标题
低温下二维远程ISING模型的动力学
Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures
论文作者
论文摘要
我们研究具有远距离耦合的二维ISING模型的低温域生长动力学：$ j（r）\ sim r^{ - （d+σ）} $，其中$ d = 2 $是维度。根据Bray-Rutenberg的预测，指数$σ$控制着特征域大小$ l（t）$，$ l（t）\ sim t^{1/z} $的代数增长，并具有增长obforts $ z = 1+σ$ for $σ<1 $和$σ<1 $和$ z = 2 $ for $ for $ for $ f in $ c $ c $ 1 $ 1 $ 1 $ 1 $。这些结果适用于低于临界温度$ t_c $的非零温度$ t $ t $ t> 0 $。我们表明，在淬火到$ t = 0 $的情况下，由于远距离交互作用，接口会经历漂移，从而使系统的动力学变得特殊。更确切地说，在这种情况下，增长指数为$ z = 4/3 $，独立于$σ$，表明它是通用数量。我们通过扩展的蒙特卡洛模拟和简化模型的分析论证来支持我们的主张。
We study the low-temperature domain growth kinetics of the two-dimensional Ising model with long-range coupling: $J(r) \sim r^{-(d+σ)}$, where $d=2$ is the dimensionality. According to the Bray-Rutenberg predictions, the exponent $σ$ controls the algebraic growth in time of the characteristic domain size $L(t)$, $L(t) \sim t^{1/z}$, with growth exponent $z=1+σ$ for $σ<1$ and $z=2$ for $σ>1$. These results hold for quenches to a non-zero temperature $T>0$ below the critical temperature $T_c$. We show that, in the case of quenches to $T=0$, due to the long-range interactions, the interfaces experience a drift which makes the dynamics of the system peculiar. More precisely we find that in this case the growth exponent takes the value $z=4/3$, independent of $σ$, showing that it is a universal quantity. We support our claim by means of extended Monte Carlo simulations and analytical arguments for simplified models.
