非顺从群上Ising相变的连续性
Continuity of the Ising phase transition on nonamenable groups
摘要：
我们严格证明，铁磁伊辛模型上的任何不顺从的凯莱图进行连续（二阶）相变的意义上说，有一个独特的吉布斯措施在临界温度。这一定理的证明是定量的，也产生幂律界的磁化和附近的临界。事实上，我们证明更一般的磁化$\langle σ_o \rangle_{β,h}^+$是一个局部的Hölder连续函数的逆温度$β$和外部字段$h$整个非负象限$(β,h)\in [0,\infty)^2$。作为我们开发的方法的第二个应用程序，我们还证明了伯努利渗流的自由能是两次可微的$p_c$上的任何传递不服从图。
英文摘要：
We prove rigorously that the ferromagnetic Ising model on any nonamenable Cayley graph undergoes a continuous (second-order) phase transition in the sense that there is a unique Gibbs measure at the critical temperature. The proof of this theorem is quantitative and also yields power-law bounds on the magnetization at and near criticality. Indeed, we prove more generally that the magnetization $\langle σ_o \rangle_{β,h}^+$ is a locally Hölder-continuous function of the inverse temperature $β$ and external field $h$ throughout the non-negative quadrant $(β,h)\in [0,\infty)^2$. As a second application of the methods we develop, we also prove that the free energy of Bernoulli percolation is twice differentiable at $p_c$ on any transitive nonamenable graph.
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