论文标题
川崎动力学在六边形晶格上的亚竞争力
Metastability for Kawasaki dynamics on the hexagonal lattice
论文作者
论文摘要
在本文中，我们分析了在六边形晶格$ \ mathbb {h}^2 $下在消失的温度限制下在川崎动力学下进化的Ising模型的亚稳定行为。令$λ\ subset \ mathbb {h}^2 $一个有限集，我们假设是任意大的。粒子对$λ$执行简单的排除，但是当它们占据相邻站点时，他们会感到绑定能量$ -U <0 $。沿着每个债券接触$λ$从外部到内部的边界，用速率$ρ= e^{ - δβ} $创建粒子，而沿着从内部到外部的每个债券沿着每个债券，粒子用速率1 an灭，其中$β$是$β$是倒数温度，$δ> 0 $是活动参数。对于{（u，\ frac {3} {2} u）}的选择$δ\，我们证明了空的（resp。\ full）hexagon是唯一的转稳性（resp. \ stable）状态。我们确定了从亚稳态到稳定状态的过渡时间的渐近性能，并给出了关键配置的描述。我们不仅显示它们的大小，而且它们的形状如何取决于热力学参数。此外，我们强调了特定晶格在分析亚稳态川崎动力学中发挥的作用，通过将该系统的不同行为与平方晶格上的相应系统进行比较。
In this paper we analyze the metastable behavior for the Ising model that evolves under Kawasaki dynamics on the hexagonal lattice $\mathbb{H}^2$ in the limit of vanishing temperature. Let $Λ\subset\mathbb{H}^2$ a finite set which we assume to be arbitrarily large. Particles perform simple exclusion on $Λ$, but when they occupy neighboring sites they feel a binding energy $-U<0$. Along each bond touching the boundary of $Λ$ from the outside to the inside, particles are created with rate $ρ=e^{-Δβ}$, while along each bond from the inside to the outside, particles are annihilated with rate 1, where $β$ is the inverse temperature and $Δ>0$ is an activity parameter. For the choice $Δ\in{(U,\frac{3}{2}U)}$ we prove that the empty (resp.\ full) hexagon is the unique metastable (resp.\ stable) state. We determine the asymptotic properties of the transition time from the metastable to the stable state and we give a description of the critical configurations. We show how not only their size but also their shape varies depending on the thermodynamical parameters. Moreover, we emphasize the role that the specific lattice plays in the analysis of the metastable Kawasaki dynamics by comparing the different behavior of this system with the corresponding system on the square lattice.
