论文标题
在树上的widom-Rowlinson模型中的动态吉布斯 - 非吉布斯过渡
Dynamical Gibbs-non-Gibbs transitions in Widom-Rowlinson models on trees
论文作者
论文摘要
我们考虑在$ d $（$ d + 1 $最近的邻居）上，在不同符号的排斥强度$β$的粒子上，在不同标志的粒子和活动参数$λ$的粒子的粒子上，我们考虑了带有旋转和孔的颗粒的软核宽洛林模型。我们在较大的排斥强度$β$的方向下分析了随时间演变的中间吉布斯度量的静态中间吉布斯度量的吉布斯特性。我们首先表明有一个动态过渡，其中对任何$ d \ geq 2 $的度量与粒子活性无关。在我们的第二个和主要结果中，我们还表明，对于大$β$，并且在粒子活动$λ$增加（假设$ d \ geq 4 $）时，一组不良配置（不连续点）的度量从零变为一个。我们的证明依靠一般的零法律来用于树上的不良配置，并引入了一组均匀的不良配置，以子树的渗透给出，我们表明在高粒子活性下这是典型的。
We consider the soft-core Widom-Rowlinson model for particles with spins and holes, on a Cayley tree of order $d$ (which has $d + 1$ nearest neighbours), depending on repulsion strength $β$ between particles of different signs and on an activity parameter $λ$ for particles. We analyse Gibbsian properties of the time-evolved intermediate Gibbs measure of the static model, under a spin-flip time evolution, in a regime of large repulsion strength $β$. We first show that there is a dynamical transition, in which the measure becomes non-Gibbsian at large times, independently of the particle activity, for any $d \geq 2$. In our second and main result, we also show that for large $β$ and at large times, the measure of the set of bad configurations (discontinuity points) changes from zero to one as the particle activity $λ$ increases, assuming that $d \geq 4$. Our proof relies on a general zero-one law for bad configurations on the tree, and the introduction of a set of uniformly bad configurations given in terms of subtree percolation, which we show to become typical at high particle activity.
