低温自旋斑模型的混合长度尺度
Mixing length scales of low temperature spin plaquettes models
摘要：
Plaquette模型是短程铁磁自旋模型，在液态玻璃化转变的动力学促进方法中起着关键作用。本文对二维元胞模型（正方形和三角形元胞模型）的热力学性质进行了严格的研究。我们证明了，对于任何正的温度，这两个模型有一个唯一的无限体积吉布斯测量指数衰减的相关性。我们分析了三个先验不同的静态相关长度的标度在小的温度制度，混合，腔和多自旋相关长度。最后，利用模型的对称性，我们确定了无限体积吉布斯测度的精确自相似性质。
英文摘要：
Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we perform a rigorous study of the thermodynamic properties of two dimensional plaquette models, the square and triangular plaquette models. We prove that for any positive temperature both models have a unique infinite volume Gibbs measure with exponentially decaying correlations. We analyse the scaling of three a priori different static correlation lengths in the small temperature regime, the mixing, cavity and multispin correlation lengths. Finally, using the symmetries of the model we determine an exact self similarity property for the infinite volume Gibbs measure.
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