$d=1$伊辛模型的更新性质
Renewal properties of the $d=1$ Ising model
摘要：
我们考虑了具有Kac势的$d=1$伊辛模型，在温度为逆的$β>1$中，平均场预言了一个具有两种可能的平衡磁化强度$\pm m_β$，$m_β>0$的相变.我们表明，当Kac标度参数$γ$是足够小的典型的自旋配置描述（通过粗粒化）由一个无限序列的连续的正负间隔的经验磁化是“接近”$m_β$和分别$-m_β$。我们证明了唯一DLR测度的相应边缘是一个更新过程。
英文摘要：
We consider the $d=1$ Ising model with Kac potentials at inverse temperature $β>1$ where mean field predicts a phase transition with two possible equilibrium magnetization $\pm m_β$, $m_β>0$. We show that when the Kac scaling parameter $γ$ is sufficiently small typical spin configurations are described (via a coarse graining) by an infinite sequence of successive plus and minus intervals where the empirical magnetization is "close" to $m_β$ and respectively $-m_β$. We prove that the corresponding marginal of the unique DLR measure is a renewal process.
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