磁场消失亚稳动力学Ising模型平衡态转变时间的渐近指数律
Asymptotic exponential law for the transition time to equilibrium of the metastable kinetic Ising model with vanishing magnetic field
摘要：
我们考虑一个Glauber动力学与伊辛模型上的一个大的二维盒子与负边界条件和一个消失的正外部磁场的限制。这个盒子的体积以磁场的倒数二次增加。我们表明，在亚临界温度和一大类的启动措施，包括措施，支持配置与宏观加自旋液滴，该系统迅速松弛到某种亚稳态平衡-在以渐近指数随机时间过渡到平衡之前，典型的配置是由负自旋海洋中的微观正相液滴组成-典型的结构是在将正相与边界分离的大轮廓内的正自旋海中的微观负相液滴。我们通过从局部弛豫时间到亚稳态和稳定平衡的边界得到这个结果。这使得有可能给出这样的过渡的路径描述，以控制混合时间的渐近行为的软容量，并给出这些能力的估计。
英文摘要：
We consider a Glauber dynamics associated with the Ising model on a large two-dimensional box with with minus boundary conditions and in the limit of a vanishing positive external magnetic field. The volume of this box increases quadratically in the inverse of the magnetic field. We show that at subcritical temperature and for a large class of starting measures, including measures that are supported by configurations with macroscopic plus-spin droplets, the system rapidly relaxes to some metastable equilibrium ---with typical configurations made of microscopic plus-phase droplets in a sea of minus spins--- before making a transition at an asymptotically exponential random time towards equilibrium ---with typical configurations made of microscopic minus-phase droplets in a sea of plus spins inside a large contour that separates this plus phase from the boundary. We get this result by bounding from above the local relaxation times towards metastable and stable equilibria. This makes possible to give a pathwise description of such a transition, to control the asymptotic behaviour of the mixing time in terms of soft capacities and to give estimates of these capacities.
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